References

[1] R. Agarwal, D. O’Reagan, I. Rachůnková, and M. Staněk, Two-point higher order BVPs with singularities in phase variable, Computers and Mathematics with Applications, 46 (2003), pp. 1799–1826.

[2] M. Ainsworth and J. Oden, A posteriori error estimation in finite element analysis, Wiley-Interscience, New York, 2000.

[3] C. Arévalo, J. López, and G. Söderlind, Linear multistep methods with constant coeffcients and step density control, to appear in J. Comp. and Appl. Math.

[4] U. Ascher, J. Christiansen, and R. Russell, A collocation solver for mixed order systems of boundary values problems, Math. Comp., 33(1978), pp. 659–679.

[5] ---, Collocation software for boundary value ODEs, ACM Transactions on Mathematical Software, 7(1981), pp. 209–222.

[6] U. Ascher and R. Spiteri, Collocation software for boundary value differential-algebraic equations, SIAM J. Sci, Comp., 4(1994), pp. 938–952.

[7] P. Bailey, W. Everitt, and A. Zettl, Computing eigenvalues of singular Sturm-Liouville problems, Results in Mathematics,20(1991),pp.391–423.

[8] K. Balla and R. März, A unified approach to linear differential algebraic equations and their adjoint equations, J. Anal. Appl., 21(2002), pp. 783–802.

[9] ---, Linear boundary value problems for differential algebraic equations, Miskolc Mathematical Notes, 5(2004), pp. 3–18.

[10] R. Bank and A. Weiser, Some a posteriori error estimators for elliptic partial differential equations, Math. Comp., 44(1985), pp. 283–301.

[11] Z. Bashir Ali, Numerical Solution of Parameter-Dependent Two-Point BVPs Using Iterated Deferred Correction, ph.d. thesis, Imperial College of Science, Technology and Medicine, London, U.K., 1998.

[12] R. Bird, W. Stewart, and E. Lightfoot, Transport phenomena, John Wiley & Sons, New York, 2002.

[13] C. Budd and R. Kuske, Localised periodic pattern for the non-symmetric generalized Swift-Hohenberg equations, Physica D, 208(2005), pp. 73–95.

[14] C. Budd, V. Rothschafer, and J. Williams, Multi-bump self-similar solutions of the complex Ginsburg Landau equations, SIAM J. Dyn. Sys., 4(2005), pp. 649–678.

[15] C. Budd and J. Williams, Parabolic monge-ampère methods for blow-up problems in several spatial dimensions, Journal of Physics A,39(2006),pp.5425–5463.

[16] C. J. Budd, Asymptotics of multibump blow-up self-similar solutions of the nonlinear Schrödinger equation, SIAM J. Appl. Math., 62(2001), pp. 801–830.

[17] C. J. Budd, V. Rottschäfer, and J. F. Williams, Multi-bump, blow-up, self-similar solutions of the complex Ginzburg-Landau equation, SIAM J. Appl. Dyn. Syst., 4(2005), pp. 649–678.

[18] P. Burrage, R. Herdiana, and K. Burrage, Predictive and PI control techniques for stochastic differential equations, to appear.

[19] C. Carstensen, Some remarks on the history and future of averaging techniques in a posteriori finite element error analysis, 84(2004), pp. 3–21.

[20] C. Christara and K. Ng, Adaptive techniques for spline collocation, Computing, 76 (2005), pp. 259–277.

[21] A. Degenhardt, Collocation for transferable differential-algebraic equations, Technical Report 1992-1, Humboldt University Berlin, 1992.

[22] R. Dokchan, Numerical integration of DAEs with harmless critical points, Humboldt University Berlin, working paper,(2007).

[23] M. Drmota, R. Scheidl, H. Troger, and E. Weinmüller, On the imperfection sensitivity of complete spherical shells, Comp. Mech., 2(1987), pp. 63–74.

[24] B. Finlayson, Nonlinear analysis in chemical engineering, McGraw-Hill Inc., New York, 1980.

[25] G. Froment and K. Bischoff, Chemical reactor analysis and design, John Wiley & Sons Inc., New York, 1990.

[26] F. Frommlet and E. Weinmüller, Asymptotic error expansions for singular boundary value problems, Math. Models Methods Appl. Sci., 11(2001), pp. 71–85.

[27] S. Golub, Measures of restrictions in inward foreign direct investment in OECD countries, OECD Economics Dept. WP Nr. 357.

[28] K. Gustafsson, Control theoretic techniques for stepsize selection in implicit Runge-Kutta methods, ACM TOMS, 20(1994), pp. 496–517.

[29] K. Gustafsson and G. Söderlind, Control strategies for the iterative solution of nonlinear equations in ODE solvers, SIAM J. Sci. Comput., 18(1997), pp. 23–40.

[30] E. Helpman, M. Melitz, and Yeaple, Export versus FDI with heterogeneous firms, Amer. Econ. Rev., 94(2004), pp. 300–316.

[31] I. Higueras and R. März, Differential algebraic equations with properly stated leading terms, Comp. Math. Appl., 48(2004), pp. 215–235.

[32] I. Higueras, R. März, and C. Tischendorf, Stability preserving integration of index-1 DAEs, Appl. Num. Math, 45(2003), pp. 175–200.

[33] ---, Stability preserving integration of index-2 DAEs, Appl. Num. Math, 45(2003), pp. 201–229.

[34] F. d. Hoog and R. Weiss, Difference methods for boundary value problems with a singularity of the first kind, SIAM J. Numer. Anal., 13(1976), pp. 775–813.

[35] ---, Collocation methods for singular boundary value problems, SIAM J. Numer. Anal., 15(1978), pp. 198–217.

[36] ---, On the boundary value problem for systems of ordinary differential equations with a singularity of the second kind, SIAM J. Math. Anal., 11(1980), pp. 41–60.

[37] ---, The application of  Runge-Kutta schemes to singular initial value problems, Math. Comp., 44 (1985), pp. 93–103.

[38] R. Kannan and D. O’Reagan, Singular and nonsingular boundary value problems with sign changing nonlinearities, J. Inequal. Appl.

[39] T. Kapitula, Existence and stability of singular heteroclinic orbits for the Ginzburg-Landau equation, Nonlinearity, 9(1996), pp. 669–685.

[40] B. Karabay, Foreign direct investment and host country policies: A rationale for using ownership restrictions, tech. report, University of Virginia, WP, 2005.

[41] G. Kitzhofer, Numerical Treatment of Implicit Singular BVPs, Ph.D. Thesis, Inst. for Anal. and Sci. Comput., Vienna Univ. of Technology, Austria, 2005. In preparation.

[42] O. Koch, Asymptotically correct errorestimationfor collocationmethodsapplied to singularboundary value problems, Numer. Math., 101(2005), pp. 143–164.

[43] A. Kopelmann, Ein kollokationsverfahren für überführbare algebro-differentialgleichunegn, Preprint 1987-151, Humboldt University Berlin, 1987.

[44] P. Kunkel and V. Mehrmann, Stability properties of differential-algebraic equations and spinstabilized discretization, preprint.

[45] ---, Differential-Algebaic Equations -Analysis and Numerical Solution, EMS Publishing House, Zürich, Switzerland, 2006.

[46] P. Kunkel and R. Stöver, Symmetric collocation methodsforlineardifferential-algebraicboundary value problems, Numerische Mathematik, 91(2002), pp. 475–501.

[47] R. Lamour, Canonical forms of DAEs, Mathematisches Forschungszentrum Oberwolfach, Report No. 18(2006).

[48] R. März, Differential algebraic equations anew, Appl. Numer. Math., 42(2002), pp. 315–335.

[49] ---, Fine decouplings of regular differential algebraic equations, Results in Mathematics, 46 (2004), pp. 57–72.

[50] ---, Projector based DAE analysis, Mathematisches Forschungszentrum Oberwolfach, Report No. 18(2006).

[51] R. März and R. Riaza, On linear differential-algebraic equations with properly stated leading terms: A-critical points, Math. Comp. Model. Dyn. Sys., 13(2004), pp. 291–314.

[52] ---, Linear differential-algebraic equations with properly stated leading term: Regular points, J. Math. Anal. Appl., 323(2006), pp. 1279–1299.

[53] ---, Linear differential-algebraic equations with properly stated leading term: A-critical points, Math. Comput. Model. Dyn. Syst., 13(2007), pp. 291–314.

[54] ---, Linear differential-algebraic equations with properly stated leading term: B-critical points, Preprint 2007-09, Humboldt University Berlin, 2007.

[55] R. März and E. Weinmüller, Solvability of boundary value problems for systems of singular differential-algebraic equations, SIAM J. Math. Anal., 24(1993), pp. 200–215.

[56] D. M. McClung and A. I. Mears, Dry-flowing avalanche run-up and run-out, J. Glaciol., 41 (1995), pp. 359–369.

[57] G. Moore, Geometric methods for computing invariant manifolds, Appl. Numer. Math.,17(1995), pp. 319–331.

[58] A. Papastavrou and R. Verfürth, A posteriori error estimators for stationary convection-diffusion problems: a computational comparison, Comput. Methods Appl. Mech. Eng.,189(2000), pp. 449–462.

[59] T. Petry, On the stability of the abramov transfer for differential-algebraic eqations of index 1, SIAM, J. Numer. Anal., 35(1998), pp. 201–216.

[60] ---, Realisierung des Newton-Kantorovich-Verfahrens für nichtlineare Algebro-Differentialgleichungen mittels Abramov-Transfer, Tech. Report, 1998.

[61] I. Rachůnková, S. Staněk, and M. Tvrdý, Singularities and Laplacians in Boundary Value Problems for Nonlinear Ordinary Differential Equations, vol. 3 of Handbook of Differential Equations. Ordinary Differential Equations, Elsevier, 2006, pp. 607–723.

[62] V. Ranade, Computational flow modeling for chemical engineering, Academic Press, San Diego, 2002.

[63] R. Riaza and R. März, A simpler construction of the matrix chain defining the tractability index of linear DAEs, Applied Mathematics Letters.

[64]--- , Linearindex-1DAEs: Regular and singularproblems,ActaAppl.Math.,84(2004),pp.24–53.
[65] L. Shampine, J. Kierzenka, and R. Reichelt, Solving Bounadry Value Problems for Ordinary Differential Equations in Matlab with bvp4C.
Available at http://www.mathworks.com/bvp_tutorial.  
[66]L. Shampine, P. Muir, and H. Xu, A User-Friendly Fortran BVP Solver. Available  at http://cs.smu.ca/˜muir/BVP_SOLVER_Files/ShampineMuirXu2006.pdf (2006).
[67] G. Söderlind, Time-step selection algorithms: adaptivity, control, and signal processing, Appl. Numer. Math.
[68] ---, Automatic control and adaptive time–stepping, Numerical Algorithms, 31(2002), p. 281.
[69] G. Söderlind and L. Wang, Adaptive time–stepping and computational stability, to appear in J. Comp. and Appl.Math.,(2007).
[70] K. Sundmacher and U. Hoffmann, Multicomponent mass and energy transport on different length scales in a packed reactive distillation column for heterogeneously catalyzed fuel ether production, Chem. Eng. Sci., 49(1994), pp. 4443–4464.
[71] J. d. Swart and G. Söderlind, On the construction of error estimators for implicit Runge–Kutta methods, J. Comp. and Appl. Math.,86(1997),p.347.
[72] R. Verfürth, A posteriori error estimates for finite element discretizations of the heat equation, Calcolo, 40(2003), pp. 195–212.
[73] ---, A posteriori error estimates for linear parabolic equations, Tech. Report, 2004.
[74] ---, Robust a posteriori error estimates for nonstationary convection-diffusion equations, SIAM J. Numer. Anal.,43(2005),pp.1783–1802.
[75] A. Verhoeven, Automatic control for adaptive time stepping in electrical circuit simulation, Philips Research Report, TN-2004/00033(2004).
[76] A. Verhoeven, T. Beelen, M. Hautus, and E. ter Maten, Digital linear control theory for automatic stepsize control, To appear.
[77] P. Wissgott, Adaptive finite element method for linear parabolic equations, Tech. Report, 2007.
[78] C.-Y. Yeh, A.-B. Chen, D. Nicholson, and W. Butler, Full-potential Korringa-Kohn-Rostoker band theory applied to the Mathieu potential, Phys. Rev. B, 42(1990), pp. 10976–10982.
[79] O. Zienkiewicz and J. Z. Zhu, A simple error estimator and adaptive procedure for practical engineering analysis, Int. J. Numer. Methods Eng.,2(1987),pp.337–357.
 

Ewa B. Weinmüller: Publications 2002-2007
For downloads and more recent publications


Refereed Journals
[EW1] O. Koch, E. Weinmüller: The Convergence of Shooting Method for Singular BVPs, Math. Comp. 72(2003), no.241,pp.289–305.

[EW2] W. Auzinger, O. Koch, and E. Weinmüller: Efficient Collocation Schemes for Singular Boundary Value Problems, Numer. Algorithms 31(2002), pp. 5-25.

[EW3] W. Auzinger, O. Koch, and E. Weinmüller: Theory and Solution Techniques for Singular Boundary Value Problems in Ordinary Differential Equations, in Parallel Processing and Applied Mathematics, M.P.R.Wyrzykowski, J.Dongarra, andJ.Wasniewski, eds., vol.2328 of Springer Lecture Notes in Computer Science, 2002, pp. 851-861.

[EW4] W. Auzinger, G. Kneisl, O. Koch, and E. Weinmüller: A Collocation Code for Boundary Value Problems in Ordinary Differential Equations, Numer. Algorithms, 33(2003), pp. 27-39.

[EW5] W. Auzinger, O. Koch, and E. Weinmüller: New Variants of Defect Correction for Boundary Value Problems in Ordinary Differential Equations, in Current Trends in Scientific Computing, Zhangxin Chen, Roland Glovinsky, Katai Li (Eds.),Contemporary Mathematics Series 329, AMS(2003), pp. 43-50.

[EW6] W. Auzinger, O. Koch, and E. Weinmüller: Analysis of a New Error Estimate for Collocation Methods Applied to Singular Boundary Value Problems,SIAMJ.Numer.Anal.42(2005), pp. 2366-2386.

[EW7] O.Koch, E.Weinmüller: Analytical and Numerical Treatment of a Singular Initial Value Problem in Avalanche Modeling, Applied Mathematics and Computation 148(2004), pp. 561-570.

[EW8] W.Auzinger, O.Koch, and E.Weinmüller: Collocation Methods for Singular Boundary Value Problems with an Essential Singularity, Large Scale Scientific Computing, I. Lirkov, S. Margenov, J.Wasniewski, P.Yalamov (Eds.), Springer Lecture Notes in Computer Science, LNCS 2907, 2003, pp. 347-354.

[EW9] W. Auzinger, H. Hofstätter, W. Kreuzer, and E. Weinmüller: Modified Defect Correction Algorithms for ODEs. Part I: General Theory, Numer. Algorithms 2, Vol. 36(2004), pp. 135-156.

[EW10] W. Auzinger, H. Hofstätter, O. Koch, W. Kreuzer, and E. Weinmüller: Superconvergent Defect Correction Algorithms, in WSEAS Transactions of Systems 4, Vol. 3(2004), pp. 1378-1383.

[EW11] W. Auzinger, H. Hofstätter, W. Kreuzer, and E. Weinmüller: Modified Defect Correction Algorithms for ODEs. Part II: Stiff IVPs, Numer. Algorithms, Vol. 40(2005), pp. 285-303.

[EW12] Ch.Budd, O.Koch, and E.Weinmüller: Computation of Self-Similar Solution Profiles for the Nonlinear Schrödinger Equation, Computing 77(2006), pp. 335-346.

[EW13] Ch. Budd, O. Koch, and E. Weinmüller: From Nonlinear PDEs to Singular ODEs, Appl. Numer. Math. 56(2006), pp. 413-422.

[EW14] W. Auzinger, O. Koch, E. Weinmüller: Efficient Mesh Selection for Collocation Methods Applied to Singular BVPs, J. Comput. Appl. Math. 1, Vol. 180(2005), pp. 213-227.

[EW15] W. Auzinger, O. Koch, D. Praetorius, and E. Weinmüller: New A-Posteriori Error Estimates for Singular Boundary Value Problems, Numer. Algorithms 40(2005), pp. 79-100.

[EW16] G. Kitzhofer, O. Koch, P. Lima, and E. Weinmüller: Efficient Numerical Solution of the Density Profile Equation in Hydrodynamics, to appear in J. Sci. Comput., published online on 26.3.2006.

[EW17] G. Kitzhofer, O. Koch, and E. Weinmüller: Pathfollowing for Essentially Singular Boundary Value Problems with Application to the Complex Ginzburg-Landau Equation, to appear in to BIT.

[EW18] W. Auzinger, E. Karner, O. Koch, and E. Weinmüller: Collocation Methods for the Solution of Eigenvalue Problems for Singular Ordinary Differential Equations, Opuscula Math. 26/2(2006), pp. 229-241.

[EW19] T. Sickenberger, E. Weinmüller, and R. Winkler: Local Error Estimates for Moderately Smooth Problems: Part I – ODEs and DAEs, BIT Numerical Mathematics 47/1(2007), pp. 157-187.

[EW20] R. März, O. Koch, D. Praetorius, E. Weinmüller: Collocation Methods for Index-1 DAEs with a critical point, Oberwolfach report No. 18/2006, ID 06016, Workshop on Differential-Algebraic Equations, 15.4. -22.4.2006, Oberwolfach, Germany.

[EW21] I. Rachunkova, O. Koch, G. Pulverer, and E. Weinmüller: On a Singular Boundary Value Probem Arising in the Theory of Shallow Membrane Caps, Math. Anal. and Appl. 332(2007), pp.523-541.

[EW22] T. Sickenberger, E. Weinmüller, and R. Winkler: Local Error Estimates for Moderately Smooth Problems: Part II – SDEa and SDAEs with Small Noise, to appear in BIT.

[EW23] S. Stanek, G. Pulverer, and E. Weinmüller: Analysis and numerical solution of positive and dead core solutions of singular two-point boundary value problems, submitted to Comp. Math. Appl.

[EW24] W. Auzinger, H. Lehner, and E. Weinmüller: A-posteriori error estimates for index-1 DAEs, submitted to Numer. Math.

Technical Reports

[EW25] W. Auzinger, G. Kneisl, O. Koch, and E. Weinmüller: A Solution Routine for Singular Boundary Value Problems,Technical Report, ANUM Preprint No.1/02,Vienna University of Technology, Austria(2002).

[EW26] W. Auzinger, G. Kneisl, O. Koch, and E.Weinmüller: SBVP 1.0 -A MATLAB Solver for Singular Boundary Value Problems, Manual, ANUM Preprint No.2/02,Vienna University of Technology, Austria(2002).
 

[EW27] W. Auzinger, O. Koch, S. Lammer, and E. Weinmüller: Variationen der Defektkorrektur zur effzienten numerischen Lösung gewöhnlicher Differentialgleichungen, Technical Report, ANUM Preprint No.8/02,Vienna University of Technology, Austria(2002).

[EW28] W. Auzinger, O. Koch, J. Petrickovic, and E. Weinmüller: Numerical Solution of Boundary Value Problems with an Essential Singularity, Technical Report, ANUM Preprint No.3/03, Vienna University of Technology,Austria(2003).

[EW29] O. Koch, A. Paul, A. Traxler, and E. Weinmüller: Effcient Numerical Solution of a Singular Initial Value Problem in Avalanche Modeling, Technical Report, ANUM Preprint No.11/02, Vienna Univeristy of Technology,Austria(2002).

[EW30] W. Auzinger, E. Karner, O. Koch, D. Praetorius, and E. Weinmüller: Globale Fehlerschätzer für Randwertprobleme mit einer Singularität der zweiten Art, ANUM PreprintNo.6/03,Vienna University of Technology, Austria(2003).

[EW31] C. Budd, O. Koch, and E. Weinmüller: From the Nonlinear Schrödinger Equation to Singular BVPs, AURORA TR2004-02, University of Technology, Vienna 2004.

[EW32] W. Auzinger, O. Koch, D. Praetorius, G. Pulverer, and E. Weinmüller: Performance of collocation software for singular BVPs, ANUM Preprint No.4/04,Vienna University of Technology, Austria (2004).

[EW33] G. Kitzhofer, O. Koch, and E. Weinmüller: Kollokationsverfahren für singuläre Randwertprobleme zweiter Ordnung in impliziter Form, ANUM Preprint No.9/04, Vienna University of Technology, Austria(2004).

[EW34] C. J. Budd, O. Koch, and E. Weinmüller: Self-Similar Blow-Up in Nonlinear PDEs, Technical ReportAURORATR2004-15, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2004.

[EW35] G. Kitzhofer, O. Koch, and E. Weinmüller: Collocation Methods for the Computation of Bubble-Type Solutions of a Singular BVP in Hydrodynamics, ANUM Preprint No.14/04,Vienna University of Technology, Austria(2004).

[EW36] T. Sickenberger, E. B. Weinmüller, and R. Winker: Local Error Estimates for Moderately Smooth ODEs and DAEs, Preprint 2006-1, Humboldt University Berlin, Germany, 2006.

[EW37] O. Koch, R. März, D. Praetorius, and E. Weinmüller: Collocation for solving DAEs with singularities, Preprint, Vienna University of Technology, Austria, 2007.

[EW38] O. Koch, R. März, D. Praetorius, and E. Weinmüller: Convergence of collocation methods for linear index 1 DAEs with singularities, to appear in Math. Comp. 

[EW39] G. Pulverer, G. Söderlind, and E. Weinmüller: Automatic grid control in adaptive BVP solvers, submtted to Numer. Alg.