List of publications
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W.Auzinger, K.N.Burdeos, M.Fallahpour, O.Koch, R.G.Mendoza, E.Weinmüller:
A numerical continuation method for parameter-dependent boundary value problems using bvpsuite 2.0,
Journal of Numerical Analysis, Industrial and Applied Mathematics (JNAIAM) 16(1-2) 1-13, 2022.
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) 100018. (DOI 10.1016/j.jcmds.2021.100018)
F.K.Auer, W.Auzinger, J.Burkotová, I.Rachůnková, E.Weinmüller:
On nonlinear singular BVPs with nonsmooth data. Part 2: Convergence of collocation methods,
Appl. Numer. Math. 171, 149-175, 2022. (DOI 10.1016/j.apnum.2021.08.016)
W.Auzinger, I.Březinová, 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) 100014. (DOI 10.1016/j.jcmds.2021.100014)
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,
in: Proceedings of the 2021 IEEE XVIIth International Conference on the Perspective Technologies and Methods in MEMS Design (MEMSTECH), 180-183, 2021. (ISSN 2573-5357)
W.Auzinger, K.Obelovska, I.Dronyuk, K.Pelekh, R.Stolyarchuk:
A Continuous Model for States in CSMA/CA-based Wireless Local Networks,
in: Proceedings of the 2nd International Conference on Data Science and Applications (ICDSA 2021). Lecture Notes in Networks and Systems, vol.287, 571-579, Springer, Singapore, 2021. (DOI 10.1007/978-981-16-5348-3_45)
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,
in: Proceedings of the 2021 IEEE 16th International Conference on the Experience of Designing and Application of CAD Systems (CADSM), Section 5: 'Models and Methods for Microelectronical Systems', 5/6-5/9, 2021. (DOI 10.1109/CADSM52681.2021.9385221)
W.Auzinger, H.Hofstätter, O.Koch, M.Quell:
Adaptive time propagation for time-dependent Schrödinger equations,
Int. J. Appl. Comput. Math. 7, 6.1-6.14, 2021. (DOI 10.1007/s40819-020-00937-9)
C.Schattauer, L.Linhart, T.Fabian, T.Jawecki, W.Auzinger, F.Libisch:
Graphene quantum dot states near defects,
Phys. Rev. B 102, 155430-1−155430-9, 2020. (DOI 10.1103/PhysRevB.102.155430)
W.Auzinger, A.A.Kytmanov, S.P.Tsarev:
A Study of Anomalies in GPS Time Series via Polynomial Filtering,
in: Proceedings of the IEEE 2020 XV'th International Scientific and Technical Conference on Computer Science and Information Technologies (CSIT 2020), Zbarazh-Lviv, Ukraine, September 23-26, 2020, 175-178.
W.Auzinger, K.Obelovska, R.Stolyarchuk:
A Revised Gomory-Hu Algorithm Taking Account of Physical Unavailability of Network Channels,
in: 'Computer Networks', P.Gaj, W.Gumiński, A.Kwiecień (Eds.), Springer International Publishing, (2020), 3-13. (DOI 10.1007/978-3-030-50719-0_1)
W.Auzinger, Y.Pelekh, M.Ihnatyshyn, R.Stolyarchuk, O.Kozar, S.Mentynskyi:
The Studying of Hydrogen Diffusion Non-Stationary Processes Near a Crack in the Field of Heterogeneous Mechanical Tensions for the Encapsulated MEMS Devices,
in: Proceedings of the IEEE 2020 XVI'th International Conference on the Perspective Technologies and Methods in MEMS Design (MEMSTECH 2020), Lviv, Ukraine, April 22-26, 2020, 164-168. (DOI 10.1109/MEMSTECH49584.2020.9109464)
W.Auzinger, P.Pukach, R.Stolyarchuk, M.Vovk:
Adaptive Numerics for Linear ODE Systems with Time-Dependent Data; Application in Photovoltaics,
in: Proceedings of the IEEE 2020 XVI'th International Conference on the Perspective Technologies and Methods in MEMS Design (MEMSTECH 2020), Lviv, Ukraine, April 22-26, 2020, 5-8.
W.Auzinger, K.Obelovska, R.Stolyarchuk:
A Modified Gomory-Hu Algorithm with DWDM-Oriented Technology,
in: Lecture Notes in Computer Science, LNCS 11958: 'Large-Scale Scientific Computing', I.Lirkov, S.Margenov (Eds.), 547-554, Springer, 2020. (DOI 10.1007/978-3-030-41032-2_63)
W.Auzinger, A.Grosz, H.Hofstätter, O.Koch:
Adaptive Exponential Integrators for MCTDHF,
in: Lecture Notes in Computer Science, LNCS 11958: 'Large-Scale Scientific Computing', I.Lirkov, S.Margenov (Eds.), 557-565, Springer, 2020. (DOI 10.1007/978-3-030-41032-2_64)
T.Jawecki, W.Auzinger, O.Koch:
Computable upper error bounds for Krylov approximations to matrix exponentials and associated \(\varphi\)-functions,
BIT Numer. Math. 60(1), 157-197, 2020. [open access] (DOI 10.1007/s10543-019-00771-6)
W.Auzinger, M.Fallahphour, O.Koch, E.Weinmüller:
Implementation of a pathfollowing strategy with an automatic step-length control: New MATLAB package bvpsuite 2.0,
[ASC Report No. 31/2019 (pdf)]
W.Auzinger, O.Koch, E.Weinmüller, S.Wurm:
Modular version bvpsuite 1.2 of the collocation MATLAB package bvpsuite 1.1,
[ASC Report No. 30/2019 (pdf)]
W.Auzinger, R.Stolyarchuk, R.Stoliarchuk:
Strongly damped Stiff Oscillator under External Force: A Case Study,
available online in: Proceedings of the 9-th International Youth Science Forum "Litteris et Artibus", Lviv Polytechnic National University, Ukraine; 22-28, 2019.
P.Pukach, V.Il'kiv, 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,
CEUR Workshop Proceedings, vol.2488, 30-42, 2019. (2nd International Workshop on Informatics and Data-Driven Medicine, IDDM 2019, Lviv, Ukraine).
Z.Nytrebych, V.Il'kiv, O.Malanchuk, W.Auzinger:
Investigation of mathematical model of acoustic wave propagation through relax environment in ultrasound diagnostics problems,
CEUR Workshop Proceedings, vol.2488, 280-289, 2019. (2nd International Workshop on Informatics and Data-Driven Medicine, IDDM 2019, Lviv, Ukraine).
I.Dronyiuk, O.Fedevych, R.Stolyarchuk, W.Auzinger:
OMNET++ and Maple software environments for IT Bachelor studies,
in: Proceedings of the 6th International Symposium on Emerging Inter-networks, Communication and Mobility, Procedia Computer Science, vol.155, 654-659, 2019.
[open access] (DOI 10.1016/j.procs.2019.08.093)
available online at www.sciencedirect.com
H.Hofstätter, W.Auzinger, O.Koch:
An algorithm for computing coefficients of words in expressions involving exponentials and its application to the construction of exponential integrators,
in 'Computer Algebra in Scientific Computing', Lecture Notes in Computer Science 11661, Springer-Verlag, 197-214, 2019. (DOI 978-3-030-26831-2_14)
W.Auzinger, H.Hofstätter, O.Koch:
Non-existence of generalized splitting methods with positive coefficients of order higher than four,
Appl. Math. Lett. 97, 48-52, 2019. (DOI 10.1016/j.aml.2019.05.017)
W.Auzinger, H.Hofstätter, O.Koch, K.Kropielnicka, P.Singh:
Time adaptive Zassenhaus splittings for the Schrödinger equation in semiclassical regime,
Appl. Math. Comput. 362, 124550, 2019. (DOI 10.1016/j.amc.2019.06.064)
[preprint at arXiv.org]
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,
in: Proceedings of the 1st International Workshop on Informatics and Data-Driven Medicine (IDDM 2018, Lviv, Ukraine), 267-274, 2018.
W.Auzinger, H.Hofstätter, O.Koch:
Symmetrized local error estimators for time-reversible one-step methods in nonlinear evolution equations,
J. Comput. Appl. Math. 356, 339-357, 2019. (DOI 10.1016/j.cam.2019.02.011)
[preprint at arXiv.org]
W.Auzinger, H.Hofstätter, O.Koch, M.Quell, M.Thalhammer:
A posteriori error estimation for Magnus-type integrators,
ESAIM: M2AN 53(1), 197-218, 2019. (DOI 10.1051/m2an/2018050)
[preprint: ASC Report No. 01/2018 (pdf)]
W.Auzinger, I.Březinová, H.Hofstätter, O.Koch, M.Quell:
Practical splitting methods for the adaptive integration of nonlinear evolution equations. Part II: Comparisons of local error estimation and step-selection strategies for nonlinear Schrödinger and wave equations,
Comput. Phys. Comm. 234, 55-71, 2019. (DOI 10.1016/j.cpc.2018.08.003)
[preprint: ASC Report No. 14/2017 (pdf)]
W.Auzinger, O.Koch:
An improved local error estimator for symmetric time-stepping schemes,
Appl. Math. Lett. 82, 106-110, 2018. (DOI 10.1016/j.aml.2018.03.001)
[ Archived at u:scholar ]
W.Auzinger, J.Burkotová, I.Rachůnková, V.Wenin:
Shooting methods for state-dependent impulsive boundary value problems, with applications,
Appl. Numer. Math. 128, 217-229, 2018. (DOI 10.1016/j.apnum.2018.02.006)
[preprint: ASC Report No. 02/2018 (pdf)]
W.Auzinger, W.Herfort, O.Koch, M.Thalhammer:
The BCH-formula and order conditions for splitting methods,
in "Lie Groups, Differential Equations, and Geometry", 71-83, Springer-Verlag, 1st ed. 2017. (ISBN: 978-3-319-62180-7)
W.Auzinger, T.Kassebacher, O.Koch, M.Thalhammer:
Convergence of a Strang splitting finite element discretization for the Schrödinger-Poisson equation,
ESAIM: M2AN 51(4), 1245-1278, 2017. (DOI 10.1051/m2an/2016059)
[preprint: ASC Report No. 40/2015 (pdf)]
W.Auzinger, O.Koch, M.Quell:
Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions,
Numer. Algor. 75(1), 261-283, 2017. [open access] (DOI 10.1007/s11075-016-0206-8)
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 Numer. Math. 57(1), 55-74, 2017. [open access] (DOI 10.1007/s10543-016-0626-9)
W.Auzinger, H. Hofstätter, O.Koch, M.Thalhammer:
Reduced order of the local error of splitting for parabolic problems,
in `Numerical Analysis and Applied Mathematics', AIP Conference Proceedings 1863, 160008 (2017). (DOI 10.1063/1.4992342)
W.Auzinger, R.Stolyarchuk, M.Tutz:
Defect correction methods, classic and new,
Visnyk of the Lviv Univ.Series Mech.Math. 82, 5-19, 2016. [open access]
W.Auzinger, R.Stolyarchuk:
A topic in the stability analysis associated with companion matrices,
Matematychni Studii 46(2), 115-120, 2016. [open access] (DOI 10.15330/ms.46.2.115-120)
W.Auzinger, W.Herfort, H.Hofstätter, O.Koch:
Setup of order conditions for splitting methods,
in 'Computer Algebra in Scientific Computing', Lecture Notes in Computer Science 9890, Springer-Verlag, 2016, 30-42. (DOI 10.1007/978-3-319-45641-6)
[preprint at arXiv.org]
W.Auzinger, H.Hofstätter, O.Koch:
Symbolic manipulation of flows of nonlinear evolution equations, with application in the analysis of split-step time integrators,
in 'Computer Algebra in Scientific Computing', Lecture Notes in Computer Science 9890, Springer-Verlag, 2016, 43-57. (DOI 10.1007/978-3-319-45641-6)
[preprint at arXiv.org]
W.Auzinger, T.Kassebacher, O.Koch, M.Thalhammer:
Adaptive splitting methods for nonlinear Schrödinger equations in the semiclassical regime,
Numer. Algor. 72(1), 1-35, 2016. (DOI 10.1007/s11075-015-0032-4)
[ Archived at u:scholar ]
W.Auzinger:
A note on similarity to contraction for stable 2x2 companion matrices,
Ukr. Math. J. 68(3), 448-457, 2016.
[Ukr. Mat. Zh. 68(3), 400-407, 2016.] (DOI 10.1007/s11253-016-1233-2)
[preprint: ASC Report No. 01/2013 (pdf)]
W.Auzinger:
Defect Correction Methods,
p. 323-332, in Encyclopedia of Applied and Computational Mathematics, Volume 1, Enquist, B. (Ed.), Springer, 2015. (ISBN: 978-3-540-70528-4)
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 No. 28/2015 (pdf)]
W.Auzinger, O.Koch, M.Quell:
Splittingverfahren für die Gray-Scott-Gleichung,
[ASC Report No. 07/2015 (pdf)]
W.Auzinger, W.Herfort:
An application of Gröbner bases to perturbed polynomial equations,
[ASC Report No. 01/2015 (pdf)]
W.Auzinger, O.Koch, M.Thalhammer:
Representation of the local error for higher-order exponential splitting schemes involving two or three sub-operators,
in `Numerical Analysis and Applied Mathematics', AIP Conference Proceedings 1648, 150003 (2015). (DOI 10.1063/1.4912433)
[preprint (pdf)]
W.Auzinger, O.Koch, M.Thalhammer:
Defect-based local error estimators for high-order splitting methods involving three linear operators,
Numer. Algor. 70(1), 61-91, 2015. (DOI 10.1007/s11075-014-9935-8)
[ Archived at u:scholar ]
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,
J. Comput. Appl. Math. 273, 182-204, 2015. (DOI 10.1016/j.cam.2014.06.012)
[ Archived at u:scholar ]
W.Auzinger, R.Stolyarchuk, M.Tutz:
Методи корекції дефекту, класичні та нові (Defect correction methods, classic and new, in Ukrainian),
[ASC Report No. 26/2014 (pdf)]
W.Auzinger, W.Herfort:
Local error structures and order conditions in terms of Lie elements for exponential splitting schemes,
Opuscula Mathematica 34(2), 243-255, 2014. [open access] (DOI 10.7494/OpMath.2014.34.2.243)
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 Numer. Math. 54, 873-900, 2014. (DOI 10.1007/s10543-014-0488-y)
[ Archived at reposiTUm ]
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,
J. Comput. Appl. Math. 255, 384-403, 2014. (DOI 10.1016/j.cam.2013.04.043)
[ Archived at u:scholar ]
I.Reichl, W.Auzinger:
Identifying Tibio-Femoral Joint Kinematics: Individual Adjustment versus Numerical Robustness,
IFAC-PapersOnLine, Mathematical Modelling, Volume #7, Part #1, 819-824, 2013. (DOI 10.3182/20120215-3-AT-3016.00145)
[preprint (pdf)]
W.Auzinger, M.Tutz:
A review of stability and error theory for collocation methods applied to linear boundary value problems,
[ASC Report No.35/2012 (pdf)]
I.Reichl, W.Auzinger:
Parameter Identification In Functional Axis Calculation For The Human Knee Joint,
in Proceedings of the 10th International Symposium on Computer Methods in Biomechanics and Biomedical Engineering (CMBBE-2012), Berlin, Germany, 2012. (ISBN: 978-0-9562121-5-3)
[preprint (pdf)]
L.Exl, W.Auzinger, S.Bance, M.Gusenbauer, F.Reichel, T.Schrefl:
Fast stray field computation on tensor grids,
J. Comput. Phys. 231(7), 2840-2850, 2012. (DOI 10.1016/j.jcp.2011.12.030)
[preprint at arXiv.org)]
W.Auzinger, O.Koch, M.Thalhammer:
Defect-based local error estimators for splitting methods, with application to Schrödinger equations, Part I: The linear case,
J. Comput. Appl. Math. 236(10), 2643-2659, 2012. (DOI 10.1016/j.cam.2012.01.001)
[ Archived at u:scholar ]
W.Auzinger, M.Łapińska:
Convergence of rational multistep methods of Adams-Padé type,
BIT Numer. Math. 52(1), 3-20, 2012. (DOI 10.1007/s10543-011-0353-1)
[preprint: ASC Report No. 05/2011 (pdf)]
W.Auzinger, M.Łapińska:
Rational multistep methods via modified \( \varphi_j \)-functions,
Proc. Appl. Math. Mech. 11, 757-758, 2011. (DOI 10.1002/pamm.201110368)
[preprint (pdf)]
W.Auzinger:
Error estimation via defect computation and reconstruction: Some particular techniques,
Journal of Numerical Analysis, Industrial and Applied Mathematics (JNAIAM) 6(1-2), 15-27, 2011.
I.Reichl, W.Auzinger, H.-B.Schmiedmayer, E.Weinmüller:
Model dependence of knee joint kinematics,
Proceedings of the XXIIIth International Society of Biomechanics Congress (ISB 2011), Brussels, Belgium, 2011. (ISSN: 1476-8259)
[preprint (pdf)]
I.Reichl, W.Auzinger, H.-B.Schmiedmayer, E.Weinmüller:
Knee joint kinematics: comparison of two optimization models with respect to data noise,
Proc. Appl. Math. Mech. 11, 111-112, 2011. (DOI 10.1002/pamm.201110047)
[preprint (pdf)] -->
I.Reichl, W.Auzinger, H.-B.Schmiedmayer, E.Weinmüller:
A study of constrained models for the kinematic analysis of the human knee joint,
Computer Methods in Biomechanics and Biomedical Engineering, 14(S1), 77-79, 2011. (DOI 10.1080/10255842.2011.592370)
[preprint (pdf)]
W.Auzinger, H.Lehner, E.Weinmüller:
An efficient asymptotically correct error estimator for collocation solutions to singular index-1 DAEs,
BIT Numer. Math. 51(1), 43-65, 2011. (DOI 10.1007/s10543-011-0321-9)
[preprint: ASC Report No. 18/2010 (pdf)]
I.Reichl, W.Auzinger, H.-B.Schmiedmayer, E.Weinmüller:
Reconstructing the knee joint mechanism from kinematic data,
Mathematical and Computer Modelling of Dynamical Systems 16(5), 403-415, 2010. [open access] (DOI 10.1080/13873954.2010.507094)
[preprint: ASC Report No. 48/2009 (pdf)]
W.Auzinger, F.Kramer:
On the stability and error structure of BDF schemes applied to linear parabolic evolution equations,
BIT Numer. Math. 50(3), 455-480, 2010. (DOI 10.1007/s10543-010-0269-1)
[preprint: ASC Report No.29/2009 (pdf)]
W.Auzinger:
Normal forms for companion matrices and contractivity in inner product norms,
[ASC Report No.24/2009 (pdf)]
W.Auzinger, H.Lehner, E.Weinmüller:
Defect-based a posteriori error estimation for index-1 DAEs with a singularity of the first kind,
in `Numerical Analysis and Applied Mathematics', AIP Conference Proceedings 1168, vol.2, 1009-1012. (DOI 10.1063/1.3241219)
[preprint (pdf)]
W.Auzinger, H.Lehner, E.Weinmüller:
Defect-based a-posteriori error estimation for differential-algebraic equations,
PAMM 7, 1023101-1023102, 2007.
[preprint (pdf)]
W.Auzinger, H.Lehner, E.Weinmüller:
Defect-based a posteriori error estimation for index-1 DAEs,
[ASC Report No.20/2007 (pdf)]
W.Auzinger, W.Herfort:
A uniform quantitative stiff stability estimate for BDF schemes,
Opuscula Mathematica 26(2), 203-227, 2006. [open access]
W.Auzinger, E.Karner, O.Koch, E.Weinmüller:
Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations,
Opuscula Mathematica 26(2), 229-241, 2006. [open access]
W.Auzinger, O.Koch, E.Weinmüller:
Efficient mesh selection for collocation methods applied to singular BVPs,
J. Comput. Appl. Math., 180(1), 213-227, 2005. (DOI 10.1016/j.cam.2004.10.013)
[ANUM Preprint No.7/04 (pdf)]
W.Auzinger, O.Koch, D.Praetorius, E.Weinmüller:
New a posteriori error estimates for singular boundary value problems,
Numer. Algor. 40(1), 79-100, 2005. (DOI 10.1007/s11075-005-3791-5)
[preprint (pdf)]
W.Auzinger, O.Koch, E.Weinmüller:
Analysis of a new error estimate for collocation methods applied to singular boundary value problems,
SIAM J. Numer. Anal. 42(6), 2366-2386, 2005. (DOI 10.1137/S0036142902418928)
[ANUM Preprint No.13/02 (pdf)]
W.Auzinger, H.Hofstätter, W.Kreuzer, E.Weinmüller:
Modified defect correction algorithms for ODEs. Part II: Stiff initial value problems,
Numer. Algor. 40(3), 285-303, 2005. (DOI 10.1007/s11075-005-5327-4)
[ANUM Preprint No.2/03 (pdf)]
W.Auzinger, H.Hofstätter, W.Kreuzer, E.Weinmüller:
Modified defect correction algorithms for ODEs. Part I: General theory,
Numer. Algor. 36(2), 135-156, 2004. (DOI 10.1023/B:NUMA.0000033129.73715.7f)
Extended version: [ANUM Preprint No.1/03 (pdf)]
W.Auzinger, H.Hofstätter, O.Koch, W.Kreuzer, E.Weinmüller:
Superconvergent defect correction algorithms,
WSEAS Transactions on Systems 4, 1378-1383, 2004.
[preprint (pdf)]
W.Auzinger, O.Koch, E.Weinmüller:
Collocation methods for boundary value problems with an essential singularity,
in Large-Scale Scientific Computing (I.Lirkov, S.Margenov, J.Wasniewski and P.Yalamov, eds.), Springer Lecture Notes in Computer Science 2907, 347-354, 2004. (DOI 10.1007/978-3-540-24588-9_39)
[preprint (pdf)]
W.Auzinger, C.Fabianek:
Iterative solution of large linear systems arising in the 3-dimensional modelling of an electric field in human thigh,
[Technical Report / ANUM Preprint No.12/04 (pdf)]
W.Auzinger, O.Koch, D.Praetorius, G.Pulverer, E.Weinmüller:
Performance of collocation software for singular BVPs,
[Technical Report ANUM Preprint No.4/04 (pdf)]
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 (eds), AMS Series in Contemporary Mathematics 329, 43-50, 2003.
[preprint (pdf)]
W.Auzinger:
Sectorial operators and normalized numerical range,
Appl. Numer. Math. 45(4), 367-388, 2003. (DOI 10.1016/S0168-9274(02)00254-4)
[article (pdf)]
W.Auzinger, G.Kneisl, O.Koch, E.Weinmüller:
A collocation code for boundary value problems in ordinary differential equations,
Numer. Algor. 33, 27-39, 2003. (DOI 10.1023/A:1025531130904)
[ANUM Preprint No.18/01 (pdf)]
W.Auzinger, E.Karner, O.Koch, D.Praetorius, E.Weinmüller:
Globale Fehlerschätzer für Randwertprobleme mit einer Singularität zweiter Art,
[Technical Report / ANUM Preprint No.6/03 (pdf)]
W.Auzinger, O.Koch, J.Petrickovic, E.Weinmüller:
Numerical solution of boundary value problems with an essential singularity,
[Technical Report / ANUM Preprint No.3/03 (pdf)]
W.Auzinger, O.Koch, E.Weinmüller:
Efficient collocation schemes for singular boundary value problems,
Numer. Algor. 31, 5-25, 2002. (DOI 10.1023/A:1021151821275)
[article (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, Vol.5: Chaos, Control and Time Series (J.M.Balthazar, P.B.Goncalves, R.F.Brasil, I.L.Caldas, F.B. Rizatto, Eds.) 127-136, 2002.
[preprint (pdf)]
W.Auzinger, O.Koch, E.Weinmüller:
Theory and solution techniques for singular boundary value problems in ordinary differential equations,
in `Parallel Processing and Applied Mathematics', Proceedings, 4th International Conference, PPAM 2001, 851-861. (Springer-Verlag, Berlin, Heidelberg, 2002.)
[article (pdf)]
W.Auzinger, O.Koch, S.Lammer, E.Weinmüller:
Variationen der Defektkorrektur zur effizienten numerischen Lösung gewöhnlicher Differentialgleichungen,
[Technical Report / ANUM Preprint No.8/02 (pdf)]
W.Auzinger, G.Kneisl, O.Koch, E.Weinmüller:
sbvp 1.0 - A MATLAB solver for singular boundary value problems,
[Technical Report / ANUM Preprint No.2/02 (pdf)]
W.Auzinger, G.Kneisl, O.Koch, E.Weinmüller:
A solution routine for singular boundary value problems,
[Technical Report / ANUM Preprint No.1/02 (pdf)]
W.Auzinger, A.Eder:
A note on Lyapunov transformation and exponential decay in linear ODE systems,
Mathematical Models and Methods in Applied Sciences (M3AS), Vol.11, No.1, 23-31, 2001. (DOI 10.1142/S0218202501000714)
[preprint (pdf)]
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 (2001), Vienna University of Technology, Austria.
[ANUM Preprint No.24/01 (pdf)]
W.Auzinger, A.Eder, R.Frank:
Extending convergence theory for nonlinear stiff problems, part II,
[Technical Report / ANUM Preprint No.22/01 (pdf)]
W.Auzinger, O.Koch, W.Polster, E.Weinmüller:
Ein Algorithmus zur Gittersteuerung bei Kollokationsverfahren für singuläre Randwertprobleme,
[Technical Report / ANUM Preprint No.21/01 (pdf)]
W.Auzinger, R.Frank, W.Kreuzer, E.Weinmüller:
Computergestützte Analyse verschiedener Varianten der Iterierten Defektkorrektur unter besonderer Berücksichtigung steifer Differentialgleichungen,
[Technical Report / ANUM Preprint No.20/01 (pdf)]
W.Auzinger, R.Frank, H.Hofstätter, E.Weinmüller:
Defektkorrektur zur numerischen Lösung steifer Anfangswertprobleme,
[Report No.131/00, Institut für Angewandte und Numerische Mathematik, TU Wien, 2000 (pdf)]
W.Auzinger, A.Eder, R.Frank:
Eine erweiterte Konvergenztheorie impliziter Runge-Kutta Verfahren für nichtlineare steife Differentialgleichungen,
[Report No.130/00, Institut für Angewandte und Numerische Mathematik, TU Wien, 2000 (pdf)]
W.Auzinger, O.Koch, P.Kofler, E.Weinmüller:
Acceleration techniques for singular initial value problems,
[Report No.129/00, Institut für Angewandte und Numerische Mathematik, TU Wien, 2000 (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,
[Report No.123/00, Institut für Angewandte und Numerische Mathematik, TU Wien, 2000 (pdf)]
W.Auzinger, O.Koch, P.Kofler, E.Weinmüller:
The application of shooting to singular boundary value problems,
[Report No.126/99, Institut für Angewandte und Numerische Mathematik, TU Wien, 2000 (pdf)]
W.Auzinger, P.Kofler, E.Weinmüller:
Steuerungsmaßnahmen bei numerischer Lösung singulärer Anfangswertaufgaben,
[Report No.124/98, Institut für Angewandte und Numerische Mathematik, TU Wien, 1998 (pdf)]
W.Auzinger, R.Frank:
B-Convergence,
in Encyclopedia of Mathematics Supplement Volume I, p.71, Kluwer Academic Publishers, 1997.
[preprint (pdf)]
W.Auzinger, R.Frank, H.J.Stetter:
Vienna contributions to the development of RK-methods,
Appl. Numer. Math. 22, 35-49, 1996. (DOI 10.1016/S0168-9274(96)00024-4)
[preprint (pdf)]
W.Auzinger, R.Frank, G.Kirlinger:
Extending convergence theory for nonlinear stiff problems, part I,
BIT Numer. Math. 36(4), 635-652, 1996. (DOI 10.1007/BF01733784)
[preprint (pdf)]
W.Auzinger, G.Kirlinger:
Kreiss resolvent conditions and strengthened Cauchy-Schwarz inequalities,
Appl. Numer. Math. 18, 57-67, 1995. (DOI 10.1016/0168-9274(95)00043-T)
[article (pdf)]
W.Auzinger, P.Trieb, E.Weinmüller:
Beschleunigte Algorithmen zur Lösung von singulären Randwertaufgaben,
Report No.113/94, Institut für Angewandte und Numerische Mathematik, TU Wien, 1994. [outline (pdf)]
W.Auzinger, R.Frank, G.Kirlinger:
Modern convergence theory for stiff initial-value problems,
J. Comput. Appl. Math. 45, 5-16, 1993. (DOI 10.1016/0377-0427(93)90260-I)
[preprint (pdf)]
W.Auzinger, R.Frank, G.Kirlinger:
An extension of B-convergence for Runge-Kutta methods,
Appl. Numer. Math. 9(2), 91-109, 1992. (DOI 10.1016/0168-9274(92)90008-2)
[preprint (pdf)]
W.Auzinger, R.Frank, E.Weinmüller:
On the efficient numerical integration of conservation laws with stiff source terms,
[Report No.94/92, Institut für Angewandte und Numerische Mathematik, TU Wien, 1992 (pdf)]
W.Auzinger, R.Frank, G.Kirlinger:
The state of the art in the convergence theory for stiff ODEs,
Proceedings, IMACS 91, Volume 1, 280-284 (Eds. R.Vichnevetsky, J.J.H.Miller, Dublin, 1991).
[preprint (pdf)]
W.Auzinger:
Error structures and extrapolation in time for parabolic problems,
Bonner Mathematische Schriften, Nr.228, 41-56, Bonn, 1991.
[preprint (pdf)]
W.Auzinger, R.Frank, G.Kirlinger:
Error structures for stiff initial value problems,
in `Numerical Treatment of Differential Equations', Proceedings, NUMDIFF-5 (Ed. K.Strehmel), Halle, 1989. (Teubner-Texte zur Mathematik 121, 1991, 16-25.)
[preprint (pdf)]
W.Auzinger:
On error structures and extrapolation for stiff systems, with application in the method of lines,
Computing 44, 331-356, 1990. (DOI 10.1007/BF02241272)
[preprint (pdf)]
W.Auzinger, R.Frank, G.Kirlinger:
A note on convergence concepts for stiff problems,
Computing 44, 197-208, 1990. (DOI 10.1007/BF02262216)
[preprint (pdf)]
W.Auzinger, R.Frank, G.Kirlinger:
Asymptotic error expansions for stiff equations: applications,
Computing 43, 223-253, 1990. (DOI 10.1007/BF02242919)
[preprint (pdf)]
W.Auzinger, R.Frank, F.Macsek:
Asymptotic error expansions for stiff equations: The implicit Euler scheme,
SIAM J. Numer. Anal. 27(1), 67-104, 1990. (DOI 10.1137/0727005)
[preprint (pdf)]
W.Auzinger, H.J.Stetter:
A study of numerical elimination for the solution of multivariate polynomial systems,
Report, Institut für Angewandte und Numerische Mathematik, TU Wien, 1989.
[report (pdf)]
W.Auzinger:
On the error structure of the implicit Euler scheme applied to stiff systems of differential equations,
Computing 43, 115-131, 1989. (DOI 10.1007/BF02241856)
[preprint (pdf)]
W.Auzinger, R.Frank:
Asymptotic expansions of the global discretization error for stiff problems,
SIAM J. Sci. Stat. Comput. 10(5), 950-963, 1989. (DOI 10.1137/0910055)
[preprint (pdf)]
W.Auzinger, R.Frank:
Asymptotic error expansions for stiff equations: An analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case,
Numer. Math. 56(5), 469-499, 1989. (DOI 10.1007/BF01396649)
[preprint (pdf)]
W.Auzinger, R.Frank:
Asymptotische Fehlerentwicklungen bei steifen Differentialgleichungen: Ergebnisse und numerische Verifikation,
ZAMM 69(4), T273-T274, 1989.
[preprint (pdf)]
W.Auzinger, R.Frank, F.Macsek:
Fehlerstrukturen bei steifen Differentialgleichungen,
ZAMM 69(4), T133-T134, 1989.
[preprint (pdf)]
W.Auzinger, R.Frank:
Asymptotic error expansions for stiff equations: The implicit midpoint rule,
[Report No.77/88, Institut für Angewandte und Numerische Mathematik, TU Wien, 1988 (pdf)]
W.Auzinger, H.J.Stetter:
An elimination algorithm for the computation of all zeros of a system of multivariate polynomial equations,
Proceedings, `International Conference on Numerical Mathematics', Singapore, 1988. (Birkhäuser ISNM 86, 1988, 11-30.)
[preprint (pdf)]
W.Auzinger:
A quantitative discrete \( H^2 \)-regularity estimate for the Shortley-Weller scheme in convex domains,
Numer. Math. 52(5) 523-537, 1988. (DOI 10.1007/BF01400890)
[preprint (pdf)]
W.Auzinger, R.Frank, F.Macsek:
On asymptotic expansions of the discretization error for stiff equations,
in `Numerical Treatment of Differential Equations', Proceedings, NUMDIFF-4 (Ed. K.Strehmel), Halle, 1987. (Teubner-Texte zur Mathematik 104, 1988, 31-39.)
[preprint (pdf)]
W.Auzinger, J.P.Monnet:
IDeC-convergence independent of error asymptotics,
BIT Numer. Math. 27(3), 350-367, 1987. (DOI 10.1007/BF01933730)
[preprint (pdf)]
W.Auzinger:
Defect correction for nonlinear elliptic difference equations,
Numer. Math. 51(2), 199-208, 1987. (DOI 10.1007/BF01396749)
[preprint (pdf)]
W.Auzinger:
Defect corrections for multigrid solutions of the Dirichlet problem in general domains,
Math. Comp. 48, 471-484, 1987. (DOI 10.1090/S0025-5718-1987-0878685-7)
[article (pdf)]
W.Auzinger, R.Frank, F.Macsek:
Asymptotic error expansions for stiff equations. Part 2: The mildly stiff case,
[Report No.68/86, Institut für Angewandte und Numerische Mathematik, TU Wien, 1986 (pdf)]
W.Auzinger, R.Frank, F.Macsek:
Asymptotic error expansions for stiff equations. Part 1: The strongly stiff case,
[Report No.67/86, Institut für Angewandte und Numerische Mathematik, TU Wien, 1986 (pdf)]
W.Auzinger, H.J.Stetter:
Accurate arithmetic results for decimal data on non-decimal computers,
Computing 35, 141-151, 1985. (DOI 10.1007/BF02260501)
[preprint (pdf)]
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.
[report (pdf)]
W.Auzinger:
Defektkorrektur für Diskretisierungen des Dirichlet-Problems in allgemeinen Gebieten,
Dissertation, TU Wien, 1984.
[text (pdf)]
W.Auzinger, H.J.Stetter:
Defect corrections and multigrid iterations,
in `Multigrid Methods', Proceedings, Köln-Porz, Nov. 1981, Lecture Notes in Mathematics 960, Springer, Berlin 1982.
[preprint (pdf)]
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