Scientific Publications
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| 1990 | 1991 | 1992 | 1993 | 1994 | 1995 | 1996 | 1997 | 1998 | 1999 |
| 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 |
| 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 |
| 2020 | 2021 | 2022 | all |
2022
Articles
F. Auer, W. Auzinger, J. Burkotova, I. Rachunkova, E. Weinmüller: On nonlinear singular BVPs with nonsmooth data. Part 2: Convergence of collocation methods, Applied Numerical Mathematics, 171 (2022), 149-175. [abstract] [www]
W. Auzinger, K. Burdeos, M. Fallahpour, O. Koch, R. Mendoza, E. Weinmüller: A numerical continuation method for parameter-dependent boundary value problems using bvpsuite 2.0, JNAIAM J. Numer. Anal. Indust. Appl. Math., 16 (2022), 1-13. [abstract] [pdf]
W. Auzinger, J. Dubois, K. Held, H. Hofstätter, T. Jawecki, A. Kauch, O. Koch, K. Kropielnicka, P. Singh, C. Watzenböck: Efficient Magnus-type integrators for solar energy conversion in Hubbard models, Journal of Computational Mathematics and Data Science (JCMDS), 2 (2022). [abstract] [pdf]
2021
Articles
W. Auzinger, I. Brezinova, A. Grosz, H. Hofstätter, O. Koch, T. Sato: Efficient adaptive exponential time integrators for nonlinear Schrödinger equations with nonlocal potential, Journal of Computational Mathematics and Data Science (JCMDS), 1 (2021). [abstract] [pdf]
W. Auzinger, H. Hofstätter, O. Koch, M. Quell: Adaptive Time Propagation for Time-Dependent Schrödinger Equations, International Journal of Applied and Computational Mathematics, 7 (2021), 6-1-6-14. [abstract] [pdf]
Proceedings
W. Auzinger, K. Obelovska, I. Dronyuk, K. Pelekh, R. Stolyarchuk: A Continuous Model for States in CSMA/CA-based Wireless Local Networks, 2nd International Conference on Data Science and Applications (ICDSA 2021), Kolkata, Indien, 10.04.2021-11.04.2021, Proceedings of the 2nd International Conference on Data Science and Applications, M. Saraswat, S. Roy, C. Chowdhury, A.H. Gandomi (Hrg.), Lecture Notes in Networks and Systems, Springer, 287 (2021), ISSN: 2367-3370, S. 571-579. [abstract] [www]
W. Auzinger, T. Jawecki, O. Koch, P. Pukach, R. Stolyarchuk, E. Weinmüller: Some Aspects on [numerical] Stability of Evolution Equations of Stiff Type, Use of Computer Algebra, MEMSTECH 2021, Polyana, 12.05.2021-16.05.2021, Proceedings of the IEEE International Conference on the Perspective Technologies and MEMS Design (MEMSTECH) Lviv, Ukraine, 2021., IEEE Ukraine Section, (2021), S. 180-183. [abstract]
P. Pukach, A. Slipchuk, W. Auzinger, R. Stolyarchuk, Y. Pukach, A. Kunynets, N. Pabyrivska: Asymptotic Method for Studying Mathematical Models of Resonant and Nonresonant Nonlinear Vibrations for Some 1D Moving Bodies, CADSM'2021, Lviv, 22.02.2021-24.02.2021, Proceedings of the 2021 IEEE 16th International Conference on the Experience of Designing and Application of CAD Systems (CADSM), IEEE, (2021), ISBN: 978-0-7381-4629-4, S. 5/6-5/9. [abstract] [www]
2020
Articles
T. Jawecki, W. Auzinger, O. Koch: Computable upper error bounds for Krylov approximations to matrix exponentials and associated phi-functions, BIT Numerical Mathematics, 60 (2020), 157-197. [abstract] [pdf]
C. Schattauer, L. Linhart, T. Fabian, T. Jawecki, W. Auzinger, F. Libisch: Graphene quantum dot states near defects, Physical Review B, 102 (2020), 1-9. [abstract] [www]
Proceedings
W. Auzinger, K. Obelovska, R. Stolyarchuk: A Modified Gomory-Hu Algorithm with DWDM-oriented Technology, 12th International Conference on Large-Scale Scientific Computations, Sozopol, 10.06.2019-14.06.2019, Proceedings of the 12th International Conference on Large-Scale Scientific Computations, Springer Lecture Notes in Computer Science (LNCS), 11958 (2020), S. 547-554. [abstract] [pdf]
W. Auzinger, R. Stolyarchuk, Y. Pelekh, O. Kozar, S. Mentynskyi, M. Ihnatyshyn: The Studying of Hydrogen Diffusion Non-Stationary Processes Near a Crack in the Field of Heterogeneous Mechanical Tensions for the Encapsulated MEMS Devices, 2020 IEEE XVIth International Conference on the Perspective Technologies and Methods in MEMS Design (MEMSTECH), IEEE Xplore, 2020, ISBN: 978-1-7281-7181-4, 164-168. [abstract] [www]
W. Auzinger, K. Obelovska, R. Stolyarchuk: A Revised Gomory-Hu Algorithm Taking Account of Physical Unavailability of Network Channels, 27th International Science Conference on Computer Networks CN2020, Gdansk, Poland, 23.06.2020-24.06.2020, Computer Networks, P. Gaj, W. Gumiń, ski, A. Kwiecień, (Hrg.), Springer International Publishing, (2020), ISBN: 978-3-030-50718-3, S. 3-13. [abstract] [pdf]
W. Auzinger, A.A. Kytmanov, S.P. Tsarev: A Study of Anomalies in GPS Time Series via Polynomial Filtering, Hauptvortrag: XV International Scientific and Technical Conference Computer Science and Information Technologies, Zbarazh-Lviv, Ukraine, Lviv, 23.09.2020-26.09.2020, Ieee Csit 2020, IEEE, (2020), S. 175-178. [abstract]
W. Auzinger, A. Grosz, H. Hofstätter, O. Koch: Adaptive Exponential Integrators for MCTDHF, 12th International Conference on Large-Scale Scientific Computations, Sozopol, 10.06.2019-14.06.2019, Proceedings of the 12th International Conference on Large-Scale Scientific Computations, Springer Lecture Notes in Computer Science (LNCS), 11958 (2020), S. 557-565. [abstract] [pdf]
Theses
M. Brunner: Local error analysis for generalised splitting methods (Supervisor: W. Auzinger), Diploma thesis, Institute of Analysis and Scientific Computing, 2020, Examination: 2020. [abstract]
A. Grosz: Exponential integrators for time-dependent multi-particle Schrödinger equations (Supervisor: W. Auzinger), Diploma thesis, Institute of Analysis and Scientific Computing, 2020, Examination: 21.04.2020. [abstract]
2019
Articles
W. Auzinger, H. Hofstätter, O. Koch, M. Quell, M. Thalhammer: A Posteriori Error Estimation for Magnus-Type Integrators, Mathematical Modelling and Numerical Analysis (M2AN), 53 (2019), 197-218. [abstract] [www] [preprint]
W. Auzinger, I. Brezinova, H. Hofstätter, O. Koch, M. Quell: Practical Splitting Methods for the Adaptive Integration of Nonlinear Evolution Equations. Part II: Comparison of Local Error Estimation and Step-Selection Strategies for Nonlinear Schrödinger and Wave Equations, Computer Physics Communications, 234 (2019), 55-71. [abstract] [www] [preprint]
W. Auzinger, H. Hofstätter, O. Koch: Non-existence of generalized splitting methods with positive coefficients of order higher than four, Applied Mathematics Letters, 97 (2019), 48-52. [abstract] [www]
W. Auzinger, H. Hofstätter, O. Koch: Symmetrized local error estimators for time-reversible one-step methods in nonlinear evolution equations, Journal of Computational and Applied Mathematics, 356 (2019), 339-357. [abstract] [www]
W. Auzinger, H. Hofstätter, O. Koch, K. Kropielnicka, P. Singh: Time adaptive Zassenhaus splittings for the Schrödinger equation in the semiclassical regime, Appl. Math. Comput., 362 [124550] (2019). [abstract] [www]
Proceedings
W. Auzinger, H. Hofstätter, O. Koch: An algorithm for computing coefficients of words in expressions envolving exponentials and its application to the construction of exponential integrators, 21st International Workshop on Computer Algebra in Scientific Computing, Moskau, 26.08.2019-30.08.2019, Computer Algebra in Scientific Computing, Springer Lecture Notes in Computer Science (LNCS), 11661 (2019), ISSN: 0302-9743, S. 197-214.
W. Auzinger, R. Stolyarchuk, R. Stoliarchuk: Strongly damped Stiff Oscillator under External Force: A Case Study, 9-th International Youth Science Forum , Litteris et Artibus, Lviv, 21.11.2019-23.11.2019, Proceedings of the 9-th International Youth Science Forum , Litteris et Artibus, (2019), ISSN: 2618-0227, S. 22-28. [abstract] [pdf]
I. Dronyuk, O. Fedevych, R. Stolyarchuk, W. Auzinger: OMNET++ and Maple software environments for IT Bachelor studies, The 6th International Symposium on Emerging Inter-networks, Communication and Mobility (EICM), Halifax, 19.08.2019-21.08.2019, The 6th International Symposium on Emerging Inter-networks, Communication and Mobility (EICM), E. Shakshuki, A. Yasar, H. Malik (Hrg.), Procedia Computer Science, 155 (2019), S. 654-659. [abstract] [pdf]
Z. Nytrebych, V. Ilkiv, O. Malanchuk, W. Auzinger: Investigation of mathematical model of acoustic wave propagation through relax environment in ultrasound diagnostics problems, 2nd International Workshop on Informatics and Data-Driven Medicine, IDDM 2019, Lviv, 11.11.2019-13.11.2019, CEUR Workshop Proceedings, CEUR-WS, 2488 (2019), ISSN: 1613-0073, S. 280-289. [abstract]
P. Pukach, V. Ilkiv, M. Vovk, O. Slyusarchuk, Y. Pukach, Y. Mylyan, W. Auzinger: On the mathematical model of nonlinear vibrations of a biologically active rod with consideration of the rheological factor, 2nd International Workshop on Informatics and Data-Driven Medicine, IDDM 2019, Lviv, 11.11.2019-13.11.2019, CEUR Workshop Proceedings, CEUR-WS, 2488 (2019), ISSN: 1613-0073, S. 30-42. [abstract]
Preprints, Technical Reports
W. Auzinger, M. Fallahpour, O. Koch, E. Weinmüller: Implementation of a pathfollowing strategy with an automatic step-length control: New MATLAB package bvpsuite2.0, ASC Report 31/2019, Institute of Analysis and Scientific Computing, TU Wien, 2019. [pdf]
W. Auzinger, O. Koch, E. Weinmüller, S. Wurm: Modular version bvpsuite1.2 of the collocation MATLAB package bvpsuite1.1, ASC Report 30/2019, TU Wien, TU Wien, 2019. [pdf]
2018
Articles
W. Auzinger, O. Koch: An improved local error estimator for symmetric time-stepping schemes, Applied Mathematics Letters, 82 (2018), 106-110. [abstract] [www]
W. Auzinger, J. Burkotova, I. Rachunkova, V. Wenin: Shooting methods for state-dependent impulsive boundary value problems, with applications, Applied Numerical Mathematics, 128 (2018), 217-229. [abstract] [www] [preprint]
Proceedings
W. Auzinger, I. Dronyuk, O. Fedevych, Y. Klishch, P. Lipinski: Information technology of traffic modeling using the Ateb-functions theory for improving service delivery in eHealth systems and networks, 1st International Workshop on Informatics & Data-Driven Medicine, Lviv, Ukraine, 28.11.2018-30.11.2018, Proceedings of the 1st International Workshop on Informatics & Data-Driven Medicine (IDDM 2018) Lviv, Ukraine, November 28-30, 2018, CEUR workshop proceedings, http://ceur-ws.org/Vol-2255/ (2018), ISSN: 1613-0073, S. 267-274. [abstract]
Preprints, Technical Reports
T. Jawecki, W. Auzinger, O. Koch: Computable strict upper bounds for Krylov approximations to a class of matrix exponentials and φ, -functions, ASC Report 23/2018, Institute of Analysis and Scientific Computing, TU Wien, 2018. [abstract] [pdf]
W. Auzinger, J. Burkotova, I. Rachunkova, V. Wenin: Shooting methods for state-dependent impulsive boundary value problems, with applications, ASC Report 2/2018, Institute of Analysis and Scientific Computing, TU Wien, 2018. [abstract] [pdf] [published 2018]
W. Auzinger, H. Hofstätter, O. Koch, M. Quell, M. Thalhammer: A Posteriori Error Estimation for Magnus-Type Integrators, ASC Report 1/2018, Institute of Analysis and Scientific Computing, TU Wien, 2018. [abstract] [pdf] [published 2019]
Theses
M. Quell: Splitting-Verfahren für nichtlineare Evolutionsgleichungen (Supervisor: W. Auzinger), Diploma thesis, Institute of Analysis and Scientific Computing, 2018, Examination: 2018. [abstract]
2017
Articles
W. Auzinger, T. Kassebacher, O. Koch, M. Thalhammer: Convergence of a Strang splitting finite element discretization for the Schrödinger-Poisson equation, Mathematical Modelling and Numerical Analysis (M2AN), 51 (2017), 1245-1278. [abstract] [www] [preprint]
W. Auzinger, H. Hofstätter, D. Ketcheson, O. Koch: Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes, BIT Numerical Mathematics, 57 (2017), 55-74. [abstract] [www] [preprint]
W. Auzinger, W. Herfort, O. Koch, M. Thalhammer: The BCH-formula and order conditions for splitting methods, in: , Lie Groups, Differential Equations, and Geometry, G. Falcone (Hrg.), Springer, 2017, (eingeladen), ISBN: 978-3-319-62180-7, S. 71-83. [abstract]
W. Auzinger, O. Koch, M. Quell: Adaptive High-Order Splitting Methods for Systems of Nonlinear Evolution Equations with Periodic Boundary Conditions, Numerical Algorithms, 75 (2017), 261-283. [abstract] [www] [preprint]
Proceedings
W. Auzinger, H. Hofstätter, O. Koch, M. Thalhammer: Reduced order of the local error of splitting for parabolic problems, 14th International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2016), Rhodos, 19.09.2016-25.09.2016, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2016 (ICNAAM-2016), AIP Conference Proceedings, 1608 (2017), ISBN: 9780735415386, S. 160008-160011. [abstract] [www]
Preprints, Technical Reports
W. Auzinger, I. Brezinova, H. Hofstätter, O. Koch, M. Quell: Practical Splitting Methods for the Adaptive Integration of Nonlinear Evolution Equations. Part II: Comparison of Local Error Estimation and Step-Selection Strategies for Nonlinear Schrödinger and Wave Equations, ASC Report 14/2017, Institute of Analysis and Scientific Computing, TU Wien, 2017. [abstract] [pdf] [published 2019]
2016
Articles
W. Auzinger, T. Kassebacher, O. Koch, M. Thalhammer: Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime, Numerical Algorithms, 72 (2016), 1-35. [abstract] [www] [preprint]
W. Auzinger, R. Stolyarchuk: A topic in the stability analysis associated with companion matrices, Matematychni Studii, 46 (2016), 115-120. [abstract] [pdf]
W. Auzinger, R. Stolyarchuk, M. Tutz: Defect correction methods, classic and new, Visnyk of the Lviv Univ.Series Mech.Math., 82 (2016), 5-19. [abstract]
W. Auzinger: A note on similarity to contraction for stable 2x2 companion matrices, Ukrainian Mathematical Journal, 68 (2016), 400-407. [abstract] [www] [preprint]
Proceedings
W. Auzinger, H. Hofstätter, O. Koch: Symbolic manipulation of flows of nonlinear evolution equations, with application in the analysis of split-step time integrators, CASC 2016: The 18th International Workshop on Computer Algebra in Scientific Computing, Bukarest, 19.09.2016-23.09.2016, Computer Algebra in Scientific Computing, V. Gerdt, W. Koepf, W. Seiler, E. Vorozhtsov (Hrg.), Lecture Notes in Computer Science, Springer-Verlag, 9890 (2016), ISSN: 0302-9743, S. 43-57. [abstract] [www]
W. Auzinger, W. Herfort, H. Hofstätter, O. Koch: Setup of order conditions for splitting methods, CASC 2016: The 18th International Workshop on Computer Algebra in Scientific Computing, Bukarest, 19.09.2016-23.09.2016, Computer Algebra in Scientific Computing, V. Gerdt, K. Wolfram, W. Seiler, E. Vorozhtsov (Hrg.), Lecture Notes in Computer Science, Springer-Verlag, 9890 (2016), ISSN: 0302-9743, S. 30-42. [abstract] [www]
2015
Articles
W. Auzinger: Defect Correction Methods, in: , Encyclopedia of Applied and Computational Mathematics, 1, B. Enquist (Hrg.), Springer Verlag, Wien, Heidelberg, New York, 2015, (eingeladen), ISBN: 978-3-540-70528-4, S. 323-332. [abstract] [www]
W. Auzinger, O. Koch, M. Thalhammer: Defect-based local error estimators for high-order splitting methods involving three linear operators, Numerical Algorithms, 70 (2015), 61-91. [abstract] [www] [preprint]
Proceedings
W. Auzinger, O. Koch, M. Thalhammer: Representation and estimation of the local error of higher-order exponential splitting schemes involving two or three sub-operators, 12th International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2014), Rhodos, 22.09.2014-28.09.2014, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2014 (ICNAAM-2014), (2015), S. 150003. [abstract] [www]
Preprints, Technical Reports
W. Auzinger, O. Koch, M. Quell: Adaptive High-Order Splitting Methods for Systems of Nonlinear Evolution Equations with Periodic Boundary Conditions, ASC Report 41/2015, Institute of Analysis and Scientific Computing, TU Wien, 2015. [pdf] [published 2017]
W. Auzinger, T. Kassebacher, O. Koch, M. Thalhammer: Convergence of a Strang splitting finite element discretization for the Schrödinger-Poisson equation, ASC Report 40/2015, Institute of Analysis and Scientific Computing, TU Wien, 2015. [pdf] [published 2017]
W. Auzinger, O. Koch, M. Schöbinger, E. Weinmüller: A new version of the code bvpsuite for singular BVPs in ODEs: Nonlinear solver and its application to m-Laplacians., ASC Report 28/2015, Institute of Analysis and Scientific Computing, TU Wien, 2015. [abstract] [pdf]
W. Auzinger, H. Hofstätter, D. Ketcheson, O. Koch: Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part I: Construction of optimized schemes and pairs of schemes, ASC Report 25/2015, Institute of Analysis and Scientific Computing, TU Wien, 2015. [abstract] [pdf] [published 2017]
W. Auzinger, O. Koch, M. Quell: Splittingverfahren für die Gray-Scott-Gleichung, ASC Report 07/2015, Institute of Analysis and Scientific Computing, TU Wien, 2015. [abstract] [pdf]
W. Auzinger, W. Herfort: An Application of Gröbner Bases to perturbed Polynomial Equations, ASC Report 01/2015, Institute of Analysis and Scientific Computing, TU Wien, 2015. [abstract] [pdf]
Theses
M. Schöbinger: A new version of a collocation code for singular BVPs: Nonlinear solver and its application to m-Laplacians (Supervisor: E. Weinmüller, W. Auzinger), Diploma thesis, Institute of Analysis and Scientific Computing, 2015, Examination: 10.10.2015. [abstract] [pdf]
2014
Articles
W. Auzinger, H. Hofstätter, O. Koch, M. Thalhammer: Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part III. The nonlinear case, Journal of Computational and Applied Mathematics, 273 (2014), 182-204. [abstract] [www] [preprint]
W. Auzinger, O. Koch, A. Saboor Bagherzadeh: Error estimation based on locally weighted defect for boundary value problems in second order ordinary differential equations, BIT Numerical Mathematics, 54 (2014), 873-900. [abstract] [www] [preprint]
W. Auzinger, W. Herfort: Local error structures and order conditions in terms of Lie elements for exponential splitting schemes, Opuscula Math., 34 (2014), 243-255. [abstract] [pdf] [preprint]
Preprints, Technical Reports
W. Auzinger, T. Kassebacher, O. Koch, M. Thalhammer: Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime, ASC Report 27/2014, Institute of Analysis and Scientific Computing, TU Wien, 2014. [abstract] [pdf] [published 2016]
W. Auzinger, O. Koch, M. Thalhammer: Defect-based local error estimators for high-order splitting methods involving three linear operators, ASC Report 22/2014, Institute of Analysis and Scientific Computing, TU Wien, 2014. [abstract] [pdf] [published 2015]
2013
Articles
W. Auzinger, O. Koch, M. Thalhammer: Defect-based local error estimators for splitting methods, with application to Schrödinger equations. Part II. Higher-order methods for linear problems, Journal of Computational and Applied Mathematics, 255 (2013), 384-403. [abstract] [www] [preprint] [preprint]
I. Reichl, W. Auzinger: Identifying Tibio-Femoral Joint Kinematics: Individual Adjustment versus Numerical Robustness, IFAC PapersOnLine, Mathematical Modelling, Volume # 7 | Part# 1 (2013), 819-824. [abstract] [www]
Proceedings
W. Auzinger: Global error estimation in exponential integrators, Modelling and Stability, edited by Dynamical System Modelling and Stability Investigation, DSMSI Dynamical System Modelling and Stability Investigation, Kiew, 2013, ISBN: 966-76-52-009, 26-27. [abstract] [pdf]
Preprints, Technical Reports
W. Auzinger, O. Koch, A. Saboor Bagherzadeh: Error estimation based on locally weighted defect for boundary value problems in second order ordinary differential equations, ASC Report 29/2013, Institute of Analysis and Scientific Computing, TU Wien, 2013. [abstract] [pdf] [published 2014]
W. Auzinger, W. Herfort: Local error structures and order conditions in terms of Lie elements for exponential splitting schemes, ASC Report 23/2013, Institute of Analysis and Scientific Computing, TU Wien, 2013. [abstract] [pdf] [published 2014]
W. Auzinger, H. Hofstätter, O. Koch, M. Thalhammer: Defect-based local error estimators for splitting methods, with application to Schrödinger equations Part III. The nonlinear case, ASC Report 19/2013, Institute of Analysis and Scientific Computing, TU Wien, 2013. [abstract] [pdf] [published 2014]
W. Auzinger: A note on similarity to contraction for stable 2x2 companion matrices, ASC Report 01/2013, Institute of Analysis and Scientific Computing, TU Wien, 2013. [abstract] [pdf] [published 2016]
Theses
G. Niederbrucker: Structured Preconditioners for Matrix-free Iterative Methods (Supervisor: W. Auzinger), Diploma thesis, Institute of Analysis and Scientific Computing, 2013.
M. Tutz: Iterierte Defektkorrektur für explizite und implizite Anfangswertprobleme erster und zweiter Ordnung, Betreuer/in (nen) (Supervisor: W. Auzinger, M. Thalhammer), Dissertation, Institute of Analysis and Scientific Computing, 2013, Rigorosum: 03.05.2013. [abstract]
2012
Articles
W. Auzinger, M. Lapinska: Convergence of rational multistep methods of Adams-Padé type, BIT Numerical Mathematics, 52 (2012), 3-20. [abstract] [www] [preprint]
W. Auzinger, O. Koch, M. Thalhammer: Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part I. The linear case, Journal of Computational and Applied Mathematics, 236 (2012), 2643-2659. [abstract] [www] [preprint] [preprint]
L. Exl, S. Bance, M. Gusenbauer, F. Reichel, T. Schrefl, W. Auzinger: Fast stray field computation on tensor grids, Journal of Computational Physics, 231 (2012), 2840-2850. [abstract] [www]
Proceedings
I. Reichl, W. Auzinger: Parameter Identification in Functional Axis Calculation for the Human Knee Joint, CMBBE 2012 (10th International Symposium on Computer Methods in Biomechanics and Biomedical Engineering), Berlin, 11.04.2012-14.04.2012, Proceedings of the 10th International Symposium on Computer Methods in Biomechanics and Biomedical Engineering (CMBBE-2012), (2012), ISBN: 978-0-9562121-5-3.
I. Reichl, W. Auzinger: Kinematic Analysis of the Human Knee Joint: Comparison of Methods for the Axis of Rotation Calculation, MATHMOD 2012 - 7th Vienna Conference on Mathematical Modelling, Wien, 14.02.2012-17.02.2012, ARGESIM Report no. S38 - MATHMOD 2012 Full Paper Preprint Volume, F. Breitenecker, I. Troch (Hrg.), (2012), 230 S.
Preprints, Technical Reports
W. Auzinger, O. Koch, M. Thalhammer: Defect-based local error estimators for splitting methods, with application to Schrödinger equations. Part II. Higher-order methods for linear problems, ASC Report 50/2012, Institute of Analysis and Scientific Computing, TU Wien, 2012. [abstract] [pdf] [published 2012] [published 2013]
W. Auzinger, M. Tutz: A review of stability and error theory for collocation methods applied to linear boundary value problems, ASC Report 35/2012, Institute of Analysis and Scientific Computing, TU Wien, 2012. [abstract] [pdf]
Theses
W. Müller: Modifizierte Kollokationsverfahren für gewöhnliche Differentialgleichungen (Supervisor: W. Auzinger), Diploma thesis, Institute of Analysis and Scientific Computing, 2012, Examination: 13.06.2012.
2011
Articles
W. Auzinger: Error estimation via defect computation and reconstruction: Some particular techniques, Journal of Numerical Analysis, Industrial and Applied Mathematics, 6 (2011), 15-27. [abstract] [pdf]
W. Auzinger, H. Lehner, E. Weinmüller: An efficient asymptotically correct error estimator for collocation solutions to singular index-1 DAEs, BIT Numerical Mathematics, 51 (2011), 43-65. [abstract] [www] [preprint]
Proceedings
W. Auzinger, M. Lapinska: Rational multistep methods via modified phi_j - functions, GAMM Jahrestagung 2011, Graz, 18.04.2011-21.04.2011, Proceedings of the GAMM 82nd Annual Scientific Conference, Graz, Austria, April 18-21, 2011, Proceedings in Applied Mathematics and Mechanics (PAMM), 11 (2011), ISSN: 1617-7061, 757 S. [abstract] [www]
W. Auzinger, I. Reichl, H. Schmiedmayer, E. Weinmüller: Knee joint kinematics: comparison of two optimization models with respect to data noise, GAMM Jahrestagung 2011, Graz, 18.04.2011-21.04.2011, Proceedings of the GAMM 82nd Annual Scientific Conference, Graz, Austria, April 18-21, 2011, 11 (2011), ISSN: 1617-7061, 111 S. [abstract] [www]
I. Reichl, W. Auzinger, H. Schmiedmayer, E. Weinmüller: A study of constrained models for the kinematic analysis of the human knee joint, 36ème Congrès de la Société de Biomécanique, Besançon, 31.08.2011-02.09.2011, Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis, 14 (2011), S1, S. 77-79. [www]
I. Reichl, W. Auzinger, H. Schmiedmayer, E. Weinmüller: Model dependence of knee joint rotation angles, Poster: ISB 2011, Brüssel, 03.07.2011-07.07.2011, XXIII ISB Congress (ISB2011) Proceedings, International Society of Biomechanics, (2011), ISSN: 1476-8259, 2 S. [www]
Preprints, Technical Reports
W. Auzinger, O. Koch, M. Thalhammer: Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part I. The linear case, ASC Report 34/2011, Institute of Analysis and Scientific Computing, TU Wien, 2011. [abstract] [pdf] [published 2012] [published 2013]
W. Auzinger, M. Lapinska: Convergence of rational multistep methods of Adams-Padé type, ASC Report 05/2011, Institute of Analysis and Scientific Computing, TU Wien, 2011. [abstract] [pdf] [published 2012]
2010
Articles
W. Auzinger, H. Schmiedmayer, I. Reichl, E. Weinmüller: Reconstructing the knee joint mechnism from kinematic data, Mathematical and Computer Modelling of Dynamical Systems, 16 (2010), 403-415. [abstract] [www]
W. Auzinger, F. Kramer: On the stability and error structure of BDF schemes applied to linear parabolic evolution equations, BIT Numerical Mathematics, 50 (2010), 455-480. [abstract] [www] [preprint]
Proceedings
W. Auzinger: Error estimation techniques based on defect computation and global reconstruction, International Conference on Numerical Analysis and Applied Mathematics, edited by American Institute of Physics, American Institute of Physics, 2010, ISBN: 978-0-7354-0831-9, 4 S. [abstract]
Preprints, Technical Reports
W. Auzinger, H. Lehner, E. Weinmüller: An efficient asymptotically correct error estimator for collocation solutions to singular index-1 DAEs, ASC Report 18/2010, Institute of Analysis and Scientific Computing, TU Wien, 2010. [abstract] [pdf] [published 2011]
Theses
L. Exl: A-posteriori Fehlerschätzung für Differentialgleichungen höherer Ordnung (Supervisor: W. Auzinger), Diploma thesis, Institute of Analysis and Scientific Computing, 2010, Examination: 2010.
M. Lapinska: Analysis of fractional-rational methods for stiff ODE systems, Betreuer/in (nen) (Supervisor: W. Auzinger, Z. Horvath), Dissertation, Institute of Analysis and Scientific Computing, 2010, Rigorosum: 07.12.2010.
G Kitzler: A posteriori Fehlerschätzer für Zweipunkt-Randwertprobleme mittels Defektkorrektur (Supervisor: W. Auzinger), Diploma thesis, Institute of Analysis and Scientific Computing, 2010, Examination: 2010.
2009
Proceedings
W. Auzinger, H. Lehner, E. Weinmüller: Defect-based a posteriori error estimation for index-1 DAEs with a singularity of the first kind, 7th International Conference on Numerical Analysis and Applied Mathematics (ICNAAM 2009), Rethymno, Kreta, Griechenland, 18.09.2009-22.09.2009, Numerical Analysis and Applied Mathematics, AIP Conference Proceedings, 1168, vol.2 (2009), S. 1009-1012. [abstract]
Preprints, Technical Reports
W. Auzinger, F. Kramer: On the stability and error structure of BDF schemes applied to linear parabolic evolution equations, ASC Report No. 29/2009, Institute of Analysis and Scientific Computing, TU Wien, 2009. [abstract] [pdf] [published 2010]
W. Auzinger: Normal forms for companion matrices and contractivity in inner product norms, ASC Report No. 24/2009, Institute of Analysis and Scientific Computing, TU Wien, 2009. [abstract] [pdf]
I. Reichl, W. Auzinger, H. Schmiedmayer, E. Weinmüller: Reconstruting the knee joint mechnism from kinematic data, ASC Report48/2009, Institute of Analysis and Scientific Computing, TU Wien, 2009. [abstract] [pdf]
2007
Proceedings
E. Weinmüller, H. Lehner, W. Auzinger: Defect-based a-posteriori error estimation for differential algebraic equations, ICIAM 2007, Zürich, 16.07.2007-20.07.2007, Iciam 07, Proceedings in Applied Mathematics and Mechanics (PAMM), Vol. 7 (2007), ISSN: 1617-7061, S. 1023101-1023102. [abstract] [pdf]
Preprints, Technical Reports
W. Auzinger, H. Lehner, E. Weinmüller: Defect-based a posteriori error estimation for index-1 DAEs, ASC Report 20/2007, Institute of Analysis and Scientific Computing, TU Wien, 2007. [abstract] [pdf]
Theses
F. Kramer: Lineare Mehrschrittverfahren angewandt auf quasi-singulär gestörte Probleme, Betreuer/in (nen) (Supervisor: W. Auzinger, C. Lubich), Dissertation, Institut für Mathematik, Universität Innsbruck, 2007, Rigorosum: 16.03.2007.
M. Moczydlowska: Modified linear multi-step methods for stiff ODEs (Supervisor: W. Auzinger, E. Weinmüller), Diploma thesis, Institute of Analysis and Scientific Computing, 2007.
2006
Articles
W. Auzinger, W. Herfort: A uniform quantitative stiff stability estimate for BDF schemes, Opuscula Math., 26 (2006), 203-227. [abstract] [pdf]
W. Auzinger, E. Karner, O. Koch, E. Weinmüller: Collocation Methods for the Solution of Eigenvalue Problems for Singular Ordinary Differential Equations, Opuscula Math., 26 (2006), 229-241. [abstract]
Theses
B. Sardy: Evaluierung der Nahtqualität beim automatisierten MAG-Schweißen mittels Strom-und Spannungsanalyse des Schweißprozesses, Betreuer/in (nen) (Supervisor: W. Auzinger, H. Strelec), Dissertation, Institute of Analysis and Scientific Computing, 2006. [abstract]
2005
Articles
W. Auzinger, O. Koch, D. Praetorius, E. Weinmüller: New A-Posteriori Error Estimates for Singular Boundary Value Problems, Numerical Algorithms, 40 (2005), 79-100. [abstract] [pdf]
W. Auzinger, O. Koch, E. Weinmüller: Analysis of a New Error Estimate for Collocation Methods Applied to Singular Boundary Value Problems, SIAM Journal on Numerical Analysis, 42 (2005), 2366-2386. [abstract] [pdf]
W. Auzinger, H. Hofstätter, W. Kreuzer, E. Weinmüller: Modified defect correction algorithms for ODEs. Part II: Stiff initial value problems, Numerical Algorithms, 40 (2005), 285-303. [abstract] [www]
W. Auzinger, O. Koch, E. Weinmüller: Efficient Mesh Selection for Collocation Methods Applied to Singular BVPs, Journal of Computational and Applied Mathematics, 180 (2005), 213-227. [abstract] [www]
2004
Articles
W. Auzinger, H. Hofstätter, O. Koch, W. Kreuzer, E. Weinmüller: Superconvergent Defect Correction Algorithms, WSEAS transactions on Systems, 3 (2004), 1378-1383. [abstract] [pdf]
W. Auzinger, H. Hofstätter, W. Kreuzer, E. Weinmüller: Modified defect correction algorithms for ODEs. Part I: General theory, Numerical Algorithms, 36 (2004), 135-156. [abstract] [www] [preprint]
Proceedings
W. Auzinger, O. Koch, E. Weinmüller: Collocation Methods for Boundary Value Problems with an Essential Singularity, Lecture Notes in Computer Science vol. 2907, Springer, Berlin Heidelberg, 2004, ISSN: 0302-9743, 347-354. [abstract] [pdf]
Preprints, Technical Reports
W. Auzinger, O. Koch, D. Praetorius, G. Pulverer, E. Weinmüller: Performance of Collocation Software for Singular BVPs, Institute for Applied and Numerical Mathematics, ANUM Preprint 04/2004, 2004,. [pdf]
W. Auzinger, C. Fabianek: Iterative Solution of Large Linear Systems Arising in the 3-Dimensional Modelling of an Electric Field in Human Thigh, ANUM Preprint No. 12/04, 2004. [abstract] [pdf]
Theses
I. Baltic: Vorkonditionierung beim Verfahren der konjugierten Gradienten mittels Mehrgitter-Relaxation (Supervisor: W. Auzinger), Diploma thesis, Institute of Analysis and Scientific Computing, 2004.
E. Karner: Design und Test neuer globaler Fehlerschätzer für Randwertprobleme mit einer Singularität zweiter Art (Supervisor: W. Auzinger), Diploma thesis, Institute of Analysis and Scientific Computing, 2004.
N. Mahmodi: Vorkonditionierung für elliptische Randwertprobleme (Supervisor: W. Auzinger), Diploma thesis, Institute of Analysis and Scientific Computing, 2004.
2003
Articles
W. Auzinger, O. Koch, E. Weinmüller: New Variants of Defect Correction for Boundary Value Problems in Ordinary Differential Equations, in: , Current Trends in Scientific Computing, Z. Chen, R. Glowinski, K. Li (Hrg.), herausgegeben von: AMS, Contemporary Mathematics, 2003, ISBN: 0-8218-3261--1, S. 43-50. [abstract]
W. Auzinger, G. Kneisl, O. Koch, E. Weinmüller: A Collocation Code for Singular Boundary Value Problems in Ordinary Differential Equations, Numerical Algorithms, 33 (2003), 27-39. [abstract] [pdf]
W. Auzinger: Sectorial operators and normalized numerical range, Applied Numerical Mathematics, 45 (2003), 367-388. [abstract] [pdf]
Preprints, Technical Reports
W. Auzinger, O. Koch, J. Petrickovic, E. Weinmüller: Numerical Solution of Boundary Value Problems with an Essential Singularity, ANUM Preprint No. 3/03, 2003. [abstract] [pdf]
W. Auzinger, H. Hofstätter, W. Kreuzer, E. Weinmüller: Modified defect correction algorithms for ODEs. Part I: General theory, ANUM Preprint No. 1/03, 2003. [abstract] [pdf] [published 2004]
W. Auzinger, E. Karner, O. Koch, D. Praetorius, E. Weinmüller: Globale Fehlerschätzer für Randwertprobleme mit einer Singularität zweiter Art, Institute for Applied and Numerical Mathematics, ANUM Preprint 06/2003, 2003,. [abstract] [pdf]
Theses
C. Fabianek: Efficient solution of large linear systems arising in the 3-dimensional modelling of an electric field, Betreuer/in (nen), Begutachter/in (nen): W. Auzinger, W. Mayr, E115 Institute for Applied and Numerical Mathematics, 2003.
J. Petrickovic: On the numerical solution of boundary value problems for systems of ordinary differential equations with a singularity of the second kind, Betreuer/in (nen): W. Auzinger, E115 Institut für Angewandte und Numerische Mathematik, 2003.
P. Schapil: Numerische Untersuchung der Stabilitätseigenschaften von BDF-und NDF-Verfahren, Betreuer/in (nen): W. Auzinger, E115 Institut für Angewandte und Numerische Mathematik, 2003.
S. Zdralovic: Untersuchung zur Stabilität von Rosenbrock-Verfahren, Betreuer/in (nen): W. Auzinger, E115 Institut für Angewandte und Numerische Mathematik, 2003.
2002
Articles
W. Auzinger, O. Koch, E. Weinmüller: Efficient Collocation Schemes for Singular Boundary Value Problems, Numerical Algorithms, 31 (2002), 5-25. [abstract] [pdf]
Proceedings
W. Auzinger, O. Koch, E. Weinmüller: Theory and Solution Techniques for Singular Boundary Value Problems in Ordinary Differential Equations, Parallel Processing and Applied Mathematics, Lecture Notes in Computer Science vol. 2328, Springer, Berlin Heidelberg, 2002, ISBN: 3-540-43792-4, 851-861. [abstract] [pdf]
W. Poth, M. Matzl, W. Auzinger, A. Steindl, H. Troger: Comparison of Displacement Versus Natural Variables for the Numerical Simulation of a String Pendulum, Nonlinear Dynamics, Chaos, Control and Their Applications to Engineering Sciences, J. Balthazar, P. Goncalves, R. Brasil, I. Caldas, F. Rizatto (Hrg.), American Academy of Mechanics, 5, 2002, ISBN S. 127-136. [abstract]
Preprints, Technical Reports
W. Auzinger, O. Koch, S. Lammer, E. Weinmüller: Variationen der Defektkorrektur zur effizienten numerischen Lösung gewöhnlicher Differentialgleichungen, ANUM Preprint No. 8/02, 2002. [pdf]
W. Auzinger, G. Kneisl, O. Koch, E. Weinmüller: SBVP 1.0 - A MATLAB Solver for Singular Boundary Value Problems, ANUM Preprint No. 2/02, 2002. [pdf]
W. Auzinger, G. Kneisl, O. Koch, E. Weinmüller: A Solution Routine for Singular Boundary Value Problems, ANUM Preprint No. 1/02, 2002. [abstract] [pdf]
Theses
S. Lammer: Die Defektkorrektur als numerisches Lösungsverfahren für gewöhnliche Differentialgleichungen, Betreuer/in (nen): W. Auzinger, E115 Institut für Angewandte und Numerische Mathematik, 2002.
2001
Articles
W. Auzinger, A. Eder: A Note on Lyapunov transformation and exponential decay in linear ODE systems, Mathematical Models and Methods in Applied Sciences (M3AS), 11 (2001), 23-31. [abstract] [www]
Proceedings
W. Auzinger, G. Kneisl, O. Koch, W. Polster, E. Weinmüller: Implementation of a Solution Routine for Singular Boundary Value Problems, ARGESIM - Working Group Simulation News S70, edited by ARGESIM, ARGESIM / ASIM, Wien, 2001. ISBN [abstract]
W. Auzinger, G. Kneisl, O. Koch, W. Polster, E. Weinmüller: Implementation of a Solution Routine for Singular Boundary Value Problems, ARGESIM Seminar S70 MATLAB/SIMULINK, Vienna, Austria, 20.05.2001, Seminarunterlagen MATLAB/SIMULINK, S70 (2001), S. 1-10.
Preprints, Technical Reports
W. Auzinger, R. Frank, W. Kreuzer, E. Weinmüller: Computergestützte Analyse verschiedener Varianten der Iterierten Defektkorrektur unter besonderer Berücksichtigung steifer Differentialgleichungen, ANUM Preprint No.20/01, 2001. [abstract] [pdf]
W. Auzinger, O. Koch, W. Polster, E. Weinmüller: Ein Algorithmus zur Gittersteuerung bei Kollokationsverfahren für singuläre Randwertprobleme, , ANUM Preprint No. 21/01, 2001. [pdf]
W. Auzinger, A. Eder, R. Frank: Extending convergence theory for nonlinear stiff problems, part II, ANUM Preprint No.22/01, 2001. [abstract] [pdf]
Theses
W. Kreuzer: Computergestützte Analyse verschiedener Varianten der iterierten Defektkorrektur unter besonderer Berücksichtigung steifer Differentialgleichungen, Betreuer/in (nen) (Supervisor: W. Auzinger), Dissertation, Institute for Applied and Numerical Mathematics, 2001.
2000
Preprints, Technical Reports
W. Auzinger, R. Frank, H. Hofstätter, E. Weinmüller: Defektkorrektur zur numerischen Lösung steifer Anfangswertprobleme, Technical Report No.131/00, Institut für Angewandte und Numerische Mathematik, 2000. [abstract] [pdf]
W. Auzinger, O. Koch, P. Kofler, E. Weinmüller: Acceleration Techniques for Singular Initial Value Problems, Technical Report No. 129/00, Institute of Applied Mathematics and Numerical Analysis, TU Wien, Austria, 2000.
W. Auzinger, A. Eder, R. Frank: Eine erweiterte Konvergenztheorie impliziter Runge-Kutta Verfahren für nichtlineare steife Differentialgleichungen, Technical Report No.130/00, Institut für Angwandte und Numerische Mathematik, 2000. [abstract] [pdf]
Theses
M. Matzl: Numerically efficient simulation of the motion of a perfectly flexible string, Betreuer/in (nen) (Supervisor: W. Auzinger), Dissertation, Institute for Applied and Numerical Mathematics, 2000.
1999
Preprints, Technical Reports
W. Auzinger, O. Koch, P. Kofler, E. Weinmüller: The Application of Shooting to Singular Boundary Value Problems, Technical Report No.126/99, Institute of Applied Mathematics and Numerical Analysis, TU Wien, Austria, 1999. [abstract] [pdf]
1998
Preprints, Technical Reports
W. Auzinger, P. Kofler, E. Weinmüller: Steuerungsmaßnahmen bei numerischer Lösung singulärer Anfangswertaufgaben, Technical Report No.124/98, Institut für Angewandte und Numerische Mathematik, 1998. [abstract] [pdf]
W. Auzinger, A. Eder, R. Frank: Convergence theory for implicit Runge-Kutta methods applied to a one-parameter family of stiff autonomous differential equations, Technical Report No.123/98, Institut für Angewandte und Numerische Mathematik, 1998. [abstract]
Theses
P. Kofler: Theorie und numerische Lösung singulärer Anfangswertprobleme gewöhnlicher Differentialgleichungen mit einer Singularität erster Art, Betreuer/in (nen) (Supervisor: E. Weinmüller, W. Auzinger), Dissertation, Institute for Applied and Numerical Mathematics, 1998.
1997
Articles
W. Auzinger, R. Frank: B-Convergence, in: , Encyclopedia of Mathematics, Supplement Vol. I, Kluwer Academic Publishers, 1997, (eingeladen), S. 71. [abstract] [pdf]
Theses
A. Eder: Konvergenztheorie für implizite Runge-Kutta Verfahren bei hoch nichtlinearen steifen Differentialgleichungen, Betreuer/in (nen) (Supervisor: W. Auzinger), Dissertation, Institute for Applied and Numerical Mathematics, 1997.
1996
Articles
W. Auzinger, R. Frank, H.J. Stetter: Vienna contributions to the development of RK-methods, Applied Numerical Mathematics, 22 (1996), 35-49. [abstract] [www]
W. Auzinger, R. Frank, G. Kirlinger: Extending convergence theory for nonlinear stiff problems, part I, BIT Numerical Mathematics, 36 (1996), 635-652. [abstract] [www]
1995
Articles
W. Auzinger, G. Kirlinger: Kreiss resolvent conditions and strengthened Cauchy-Schwarz inequalities, Applied Numerical Mathematics, 18 (1995), 57-67. [abstract] [pdf]
Theses
C. Fichtenbauer: Beschleunigte Algorithmen bei steifen Anfangswertproblemen, Betreuer/in (nen) (Supervisor: W. Auzinger), Dissertation, Institute for Applied and Numerical Mathematics, 1995.
A. Kuhn: Numerische Behandlung von , Tethered satellite systems, unter besonderer Berücksichtigung längssteifer Verbindungsseile, Betreuer/in (nen) (Supervisor: W. Auzinger), Dissertation, Institute for Applied and Numerical Mathematics, 1995.
1994
Preprints, Technical Reports
W. Auzinger, P. Trieb, E. Weinmüller: Beschleunigte Algorithmen zur Lösung von singulären Randwertaufgaben, Technical Report No.113/94, Institut für Angewandte und Numerische Mathematik, 1994. [abstract]
1993
Articles
W. Auzinger, R. Frank, G. Kirlinger: Modern convergence theory for stiff initial value problems, Journal of Computational and Applied Mathematics, 45 (1993), 5-16. [abstract] [www]
1992
Articles
W. Auzinger, R. Frank, G. Kirlinger: An extension of B-convergence for Runge-Kutta methods, Applied Numerical Mathematics, 9 (1992), 91-109. [abstract] [www]
Preprints, Technical Reports
W. Auzinger, R. Frank, E. Weinmüller: On the efficient numerical integration of conservation laws with stiff source terms, Technical Report No.94/92, Institut für Angewandte und Numerische Mathematik, 1992. [abstract] [pdf]
1991
Proceedings
W. Auzinger: Error structures and extrapolation in time for parabolic problems, Extrapolation and Defect Correction (Bonner Mathematische Schriften, Nr. 228), H.W. Alt et al. (Hrg.), edited by GAMM, GAMM, Bonn, 1991, ISBN S. 41-56. [abstract] [pdf]
W. Auzinger, R. Frank, G. Kirlinger: The state of the art in the convergence theory for stiff ODEs, IMACS '91: Proceedings of the IMACS World Congress on Computation and Applied Mathematics, R. Vichnevetsky, J.J.H. Miller (Hrg.), XXX, Dublin, 1991, ISBN S. 280-284. [abstract]
1990
Articles
W. Auzinger, R. Frank, F. Macsek: Asymptotic error expansions for stiff equations: The implicit Euler scheme, SIAM Journal on Numerical Analysis, 27 (1990), 67-104. [abstract] [www]
W. Auzinger: Error structures and extrapolation for stiff systems, with application in the method of lines, Computing, 44 (1990), 331-356. [abstract] [www]
W. Auzinger, R. Frank, G. Kirlinger: Asymptotic error expansions for stiff equations: applications, Computing, 43 (1990), 223-253. [abstract] [www]
W. Auzinger, R. Frank, G. Kirlinger: A note on convergence concepts for stiff problems, Computing, 44 (1990), 197-208. [abstract] [www]
1989
Articles
W. Auzinger: On the error structure of the implicit Euler scheme applied to stiff systems of differential equations, Computing, 43 (1989), 115-131. [abstract] [www]
W. Auzinger, R. Frank: Asymptotic error expansions for stiff equations: An analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case, Numerische Mathematik, 56 (1989), 469-499. [abstract] [www]
W. Auzinger, R. Frank: Asymptotic expansions of the global discretization error for stiff problems, SIAM Journal on Scientific Computing, 10 (1989), 950-963. [abstract] [www]
W. Auzinger, R. Frank: Asymptotische Fehlerentwicklungen bei steifen Differentialgleichungen: Ergebnisse und numerische Verifikation, ZAMM Z. Angew. Math. Mech. - Zeitschrift für Angewandte Mathematik und Mechanik, 69 (1989), 273-274. [abstract] [pdf]
W. Auzinger, R. Frank, F. Macsek: Fehlerstrukturen bei steifen Differentialgleichungen, ZAMM Z. Angew. Math. Mech. - Zeitschrift für Angewandte Mathematik und Mechanik, 69 (1989), 133-134. [abstract] [pdf]
Preprints, Technical Reports
W. Auzinger, H.J. Stetter: A study of numerical elimination for the solution of multivariate polynomial systems, Technical Report, Institut für Angewandte und Numerische Mathematik, 1989. [abstract] [pdf]
1988
Articles
W. Auzinger: A quantitative discrete H^2-regularity estimate for the Shortley-Weller scheme in convex domains, Numerische Mathematik, 52 (1988), 523-537. [abstract] [www]
Proceedings
W. Auzinger, H.J. Stetter: An elimination algorithm for the computation of all zeros of a system of multivariate polynomial equations, ISMN 86 - Proceedings, `International Conference on Numerical Mathematics', Singapore, 1988. ISBN , Birkhäuser, 1988, 11-30. [abstract] [pdf]
W. Auzinger, R. Frank, F. Macsek: On asymptotic expansions of the discretization error for stiff equations, `Numerical Treatment of Differential Equations', Proceedings der NUMDIFF-4, Halle 1987 (Teubner-Texte zur Mathematik 104), K. Strehmel (Hrg.), B.G.Teubner, 1988, ISBN S. 31-39. [abstract] [pdf]
Preprints, Technical Reports
W. Auzinger, R. Frank: Asymptotic error expansions for stiff equations: The implicit midpoint rule, Technical Report No.77/88, Institut für Angewandte und Numerische Mathematik, 1988. [abstract] [pdf]
1987
Articles
W. Auzinger: Defect correction for nonlinear elliptic difference equations, Numerische Mathematik, 51 (1987), 199-208. [abstract] [www]
W. Auzinger: Defect corrections for multigrid solutions of the Dirichlet problem in general domains, Mathematics of Computation, 48 (1987), 471-484. [abstract] [www]
W. Auzinger, J.P. Monnet: IDeC-convergence independent of error asymptotics, BIT Numerical Mathematics, 27 (1987), 350-367. [abstract] [www]
1986
Preprints, Technical Reports
W. Auzinger, R. Frank, F. Macsek: Asymptotic error expansions for stiff equations. Part 2: The mildly stiff case, Technical Report Nr. 68/86, Institut für Angewandte und Numerische Mathematik, 1986. [abstract]
W. Auzinger, R. Frank, F. Macsek: Asymptotic error expansions for stiff equations. Part 1: The strongly stiff case, Technical Report Nr. 67/86, Institut für Angewandte und Numerische Mathematik, 1986. [abstract]
1985
Articles
W. Auzinger, H.J. Stetter: Accurate arithmetic results for decimal data on non-decimal computers, Computing, 35 (1985), 141-151. [abstract] [www]
Preprints, Technical Reports
W. Auzinger: DCMG01: A multigrid code with defect correction to solve \Delta U - c (x, y)U = f (x, y) on \Omega, U = g (x, y) on \partial\Omega, on nonrectangular bounded domains \Omega with high accuracy, Arbeitspapiere der GMD, Nr. 127, 1985. [abstract]
1984
Theses
W. Auzinger: Defektkorrektur für Diskretisierungen des Dirichlet-Problems in allgemeinen Gebieten, Betreuer/in (nen) (Supervisor: H.J. Stetter et al.), Dissertation, Institute for Applied and Numerical Mathematics, 1984. [abstract]
1982
Proceedings
W. Auzinger, H.J. Stetter: Defect corrections and multigrid iterations, `Multigrid Methods', Proceedings, Köln-Porz, Nov. 1981, Lecture Notes in Mathematics 960, Springer, Berlin, 1982. ISBN [abstract] [pdf]
1981
Theses
W. Auzinger: Extrapolation des lokalen Diskretisierungsfehlers beim Multigrid-Verfahren (Supervisor: H.J. Stetter), Diploma thesis, Institut für Numerische Mathematik, 1981, Examination: 1981.