Publications

To download a paper click on its title. Abstracts are marked by . In case of difficulties contact me at mailto:e.weinmueller@tuwien.ac.at, I will be happy to help you.

Preprints

• G. Hastermann, L. Morgado, P. Lima, E. B. Weinmüller: Numerical Solution of the Density Profile Equation with p-Laplacians, submitted to Numer. Algorithms.
   

• P. Amodio, T. Levitina, G. Settanni, E.B. Weinmüller: On the Calculation of the Finite Hankel Transform Eigenfunctions, submitted to J. Appl. Math. Comput.
   

• A. Dick, O. Koch, R. März, E. Weinmüller, Convergence of Collocation Schemes for Nonlinear Index 1 DAEs with a Singular Point, submitted to Math. Comp.
   

Refereed Papers

• A. Feichtinger, I. Rachunkova, S. Stanek, E. B. Weinmüller, Periodic BVPs in ODEs with time singularities, Comp. Math. Appl. 64 (2011), pp. 2058-2070.
   

• G. Pulverer, G. Söderlind, E. Weinmüller, Automatic Grid Control in Adaptive BVP Solvers, Numer. Algorithms 56 (2011), pp. 61-92.
   

• A. Dick, O. Koch, R. März, E. B. Weinmüller, Collocation Schemes for Nonlinear Index 1 DAEs with a Singular Point, Proceeding of ICNAAM 2011, Halkidiki, Greece, September 2011.
   

• W. Auzinger, H. Lehner, E. B. Weinmüller, Defect-based a posteriori error estimation for index-1 DAEs, BIT 51 (2011), pp. 43-65.
   

• R. Hammerling, O. Koch, C. Simon, E. B. Weinmüller, Numerical Treatment of Singular ODE EVPs Using bvpsuite, Proceedings of ICNAAM 2010, Rhodes, Greece 2010. AIP Conference Proceeding Volume 1281, Volumes I, II, & III, Editors: T.E. Simos, G. Psihoyios, Ch. Tsitouras, 2010 American Institute of Physics, CD-ROM ISBN: 978-0-7354-0831-9.

• G. Kitzhofer, O. Koch, G. Pulverer, Ch. Simon, E. B. Weinmüller, Numerical Treatment of Singular BVPs: The New Matlab Code bvpsuite,  JNAIAM J. Numer. Anal. Indust. Appl. Math., 5(2010), pp. 113-134.

• I. Reichl, W. Auzinger, H.-B. Schmiedmayer, E. B. Weinmüller, Reconstructing the knee joint mechanism from kinematic data, Math. Comput. Model. Dyn. Syst.:  Methods, Tools and Applications in Engineering and Related Sciences, 16(2010), pp. 403-415, doi:10.1080/13873954.2010.507094.
   

• I. Rachunkova, G. Pulverer, E. B. Weinmüller, A unified approach to singular problems arising in the membran theory, Math. Anal. and Appl. 55(2010), pp. 47-75.
   

• G. Pulverer, S. Stanek, E. B. Weinmüller, Analysis and numerical solution of positive and dead core solutions of singular Sturm-Liouville problems, Adv. Difference Equ., Volume 2010 (2010), Article ID 969536, 37 pages, doi:10.1155/2010/969536.

• I. Rachunkova, S. Stanek, E. Weinmüller, M. Zenz, Neumann problems with time singularities, Comp. Math. Appl. 60 (2010), pp. 722-733.
   

• R. Hammerling, O. Koch, C. Simon, E. B. Weinmüller, Numerical Solution of Singular ODE Eigenvalue Problems in Electronic Structure Computations, J. Comp. Phys. 181(2010), pp. 1557-1561.
   

• O. Koch, R. März, D. Praetorius, E. Weinmüller, Collocation Methods for Index 1 DAEs with a Singularity of the First Kind, Math. Comp. 79(2010), pp. 281-304.
   

• J. Cash, G. Kitzhofer, O. Koch, G. Moore, E. Weinmüller, Numerical Solution of Singular Two Point BVPs, JNAIAM J. Numer.  Anal. Indust. and Appl. Math. 4(2009), pp. 129-149, published online 15.6.2009.
   

• I. Rachunkova, S. Stanek, E. B. Weinmüller, Limit properties of solutions of singular second-order differential equations,  Boundary Value Problems, Volume 2009 (2009), Article ID 905769, 28 pages, doi:10.1155/2009/905769.
   

• G. Kitzhofer, O. Koch, E. B. Weinmüller, Pathfollowing for Essentially Singular Boundary Value Problems with Application to the Complex Ginzburg-Landau Equation, BIT Numer. Math. 49(2009), pp. 217-245.
  

• T. Sickenberger, E. B. Weinmüller, R. Winkler, Local Error Estimates for Moderately Smooth Problems: Part II -- SDEa and SDAEs with Small Noise, BIT Numer. Math. 49(2009), pp. 217-245. 
   

• B. Karabay, G. Pulverer, E. Weinmüller, Foreign Ownership Restrictions: A Numerical Approach, published oline in Computational Economics 33(2009), pp. 361-388, DOI 10.1007/s10614-008-9163-1, 2008.
   

• W. Auzinger, H. Lehner, E. B. Weinmüller, Defect-based a-posteriori error estimation for differential-algebraic equations,  Pamm Proc. Appl. Math. Mech. 7(2007), pp. 1023101-1023102, Proceedings of ICIAM 2007, Zürich July 2007. 
   

• S. Stanek, G. Pulverer, E. B. Weinmüller, Analysis and numerical solution of positive and dead core solutions of singular two-point boundary value problems, Comp. Math. Appl. 56(2008), pp. 1820-1837.

• I. Rachunkova, O. Koch, G. Pulverer, E. B. Weinmüller, On a singular boundary value problem arising in the theory of shallow membrane caps, Math. Anal. and Appl. 332(2007), pp. 523-541.
   

• R. März, O. Koch, D. Praetorius, E. B. Weinmüller, Collocation Methods for Index-1 DAEs with a critical point, Oberwolfach Report No. 18/2006, ID 06016, of the Workshop on Differential-Algebraic Equations, 15.4. - 22.4.2006, Germany, pp. 81-84, see http://www.mfo.de/
   

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

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

• Ch. Budd, O. Koch, E. Weinmüller, Computation of Self-Similar Solution Profiles for the Nonlinear Schrödinger Equation, Computing 77 (2006), pp. 335-346, published online 20th April 2006, see http://dx.doi.org/10.1007/s00607-005-0157-8
  

• G. Kitzhofer, O. Koch, P. Lima, E. Weinmüller, Efficient Numerical Solution of the Density Profile Equation in Hydrodynamics, J. Sci. Comput., 32(2007), pp. 411-424, published online 26th March 2006, see http://dx.doi.org/10.1007/s10915-005-9020-5
   

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

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

• W. Auzinger, O. Koch, E. Weinmüller, Analysis of a New Error Estimate for Collocation Methods Applied to Singular Boundary Value Problem, SIAM J. Numer. Anal. 42(2005), pp. 2366-2386.
  

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

• 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.
  

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

• W. Auzinger, H. Hofstätter, O. Koch, W. Kreuzer, E. Weinmüller, Superconvergent Defect Correction Algorithms, in WSEAS Transactions on Systems 4, Vol. 3(2004), pp. 1378-1383.
  

• O. Koch, E. Weinmüller, Analytical and Numerical Treatment of a Singular Initial Value Problem in Avalanche Modeling, Appl. Math. Comp. 148(2004), pp. 561-570.
  

• W. Auzinger, O. Koch, E. B. 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, AMS (2003), pp. 43-50.
  

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

• W. Auzinger, O. Koch, 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.
   

• O. Koch, E. B. Weinmüller: The Convergence of Shooting Method for Singular BVPs, Math. Comp. 72 (2003), no. 241, pp. 289-305.
  

• W. Auzinger, O. Koch, E. B. Weinmüller: Efficient Collocation Schemes for Singular Boundary Value Problems, Numerical Algorithms 31(2002), pp. 5-25.
  

• W. Auzinger, O. Koch, E. B. Weinmüller: Theory and Solution Techniques for Singular Boundary Value Problems in Ordinary Differential Equations, Parallel Processing and Applied Mathematics, M. P. R. Wyrzykowski, J. Dongarra, and J. Wasniewski, eds., vol. 2328 of Springer Lecture Notes in Computer Science (2002), pp. 851-861.
   
• O. Koch, E. B. Weinmüller, Iterated Defect Correction for the Solution of Singular IVPs, SIAM, J. Numer. Anal. 38 (2001), pp. 1784-1799.
   
• O. Koch, P. Kofler, E. B. Weinmüller, Initial Value Problems for Systems of Ordinary First and Second Order Differential Equations with a Singularity of the First Kind, Analysis 21 (2001), pp. 373-389.
   
•  F. Frommlet, E. B. Weinmüller, Asymptotic Error Expansions for Singular Boundary Value Problems, Math. Models and Meth. in Appl. Sci. 11 (2001), pp. 71-85.
   
• O. Koch, E. B. Weinmüller, Acceleration Techniques for Singular Initial Value Problems, N. Mastorakis (Ed.),Problems in Modern Applied Mathematics, World Scientific and Engineering Society Press, 2000.
   
• O. Koch, P. Kofler, E. B. Weinmüller, The Implicit Euler Method for the Numerical Solution of  Singular Initial Value Problems, Appl. Num. Math. 34 (2000), pp. 231-252.
   
• P. Kofler, E. B. Weinmüller, Numerical Treatment of Singular Boundary and Initial Value Problems, Proceedings of Recent Advances in Applied Mathematics ("RAAM'96"), Kuwait City, Kuwait 1996. 
   
• W. Linzer, K. Ponweiser, P. Szmolyan, E. B. Weinmüller, Numerical Simulation of a Natural Circulation Steam Generator, Annals of Num. Math. 1, pp. 483-490 (1994). 
   
• R. März, E. B. Weinmüller, Solvability of Boundary Value Problems for Systems of Singular Differential-Algebraic Equations, SIAM J. Math. Anal. 24, pp. 200-215 (1993).
   
• W. Linzer, K. Ponweiser, P. Szmolyan, E. B. Weinmüller, Ein Beitrag zum numerischen Verhalten von Naturumlauf-Dampferzeugern, Fortschritt-Berichte VDI (Verein Deutscher Ingenieure), Reihe 6, Nr. 284, Düsseldorf, Germany 1993.
   
• W. Linzer, K. Ponweiser, P. Szmolyan, E. B. Weinmüller, Dynamisches Verhalten von Naturumlauf-Dampferzeugern, BWK (Brennstoff, Wärme, Kraft), Zeitschrift des VDI (Verein Deutscher Ingenieure) für Energietechnik und Energiewirtschaft, 7/8, VDI Verlag, Düsseldorf, Germany 1993.
   
• E. B. Weinmüller, Stability of Singular Boundary Value Problems and Their Discretization by Finite Differences, SIAM J. Numer. Anal. 26, pp. 180-213 (1989).
   
• E. B. Weinmüller, R. Winkler, Path-following Algorithm for Singular Boundary Value Problems, ZAMM 68, pp. 527-537 (1988).
   
• M. Drmota, R. Scheidl, H. Troger, E. B. Weinmüller, On the Imperfection Sensitivity of Complete Spherical Shells, Comp. Mech. 2, pp. 63-74 (1987).
   
• M. Gräff, E. B. Weinmüller, Testing of Error Estimation Procedures for Boundary Value Problems with a Singularity of the First Kind, Proceedings of the Annual Seminar "Oscillation, Bifurcation, Chaos", Toronto, Canada 1986.
   
• E. B. Weinmüller, On the Numerical Solution of Singular Boundary Value Problems of Second Order by a Difference Method, Math. Comp. 46, pp. 93-117 (1986).
   
• E. B. Weinmüller, On the Condition of Singular Boundary Value Problems, Appl. Math. Comp. 31, pp. 555-573 (1989).
   
• E. B. Weinmüller, Collocation for Singular Boundary Value Problems of Second Order, SIAM J. Numer. Anal. 23, pp. 1062-1095 (1986).
   
• M. Gräff, R. Scheidl, H. Troger, E. B. Weinmüller, An Investigation of the Complete Post-Buckling Behavior of Axisymmetric Spherical Shells, ZAMP 36, pp. 803-821 (1985).
   
• E. B. Weinmüller, On the Boundary Value Problems for Systems of Ordinary Second Order Differential Equations with a Singularity of the First Kind, SIAM J. Math. Anal. 15, pp. 287-307 (1984).
   
• E. B. Weinmüller, A Difference Method for a Singular Boundary Value Problem of Second Order, Math. Comp. 42, pp. 441-464 (1984).
   
• H. J. Stetter, E. B. Weinmüller, On the Error Control in ODE Solvers with Local Extrapolation, Computing 27, pp. 169-177 (1981).
   
• E. B. Weinmüller, Ideal Flow in Turbine Blades, Master Thesis, Proceedings of the Annual Meeting of Polish Engineering Society, University of Technology, Poznan, Poland 1974.

Technical reports

• R. Hammerling, O. Koch, Ch. Simon, and E. Weinmüller, Numerical Solution of Singular Eigenvalue Problems for ODEs with a Focus on Problems Posed on Semi-Infinite Intervals, ASC Preprint 08/2010, Vienna University of Technology, Austria (2010).
   

• G. Kitzhofer, O. Koch, G. Pulverer, Ch. Simon, E. B. Weinmüller, BVPSUITE: A New Matlab Solver for Singular Implicit Boundary Value Problems, ASC Preprint 35/2009, Vienna University of Technology, Austria (2009).

• D. Praetorius, E. B. Weinmüller, P. Wissgott, A Space-Time Adaptive Algorithm for Linear Parabolic Problems,
  ASC Preprint 07/2008, Vienna University of Technology, Austria (2008).
   

• T. Sickenberger, E. B. Weinmüller, R. Winkler, Local Error Estimates for Moderately Smooth Problems: Part II -- SDEa and SDAEs with Small Noise, Preprint 2007-7, Humboldt University Berlin, Germany 2007. 
   

• O. Koch, R. März, D. Praetorius, E. B. Weinmüller, Collocation for Solving DAEs with Singularities, Technical Report, ASC Preprint 32/2007, Vienna University of Technology, Austria (2007).
   

• T. Sickenberger, E. B. Weinmüller, R. Winkler, Local Error Estimates for Moderately Smooth ODEs and DAEs, Technical Report, Preprint 2006-1, Humboldt University, Berlin, Germany.
   

• G. Kitzhofer, O. Koch, E. B. Weinmüller, Collocation Methods for the Computation of Bubble-Type Solutions of a Singular BVP in Hydrodynamics, Technical Report, ANUM Preprint No. 14/04, Vienna University of Technology, Austria (2004).
  
  
• C.J. Budd, O. Koch, E. B. Weinmüller, Self-Similar Blow-Up in Nonlinear PDEs, Technical Report AURORA TR2004-15, Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria, 2004.
  

• G. Kitzhofer, O. Koch, E. Weinmüller, Kollokationsverfahern für singuläre Randwertprobleme zweiter Ordnung in impliziter Form, Technical Report, ANUM Preprint No. 9/04, Vienna University of Technology, Austria (2004).
   

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

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

• W. Auzinger, E. Karner, O. Koch, E. Weinmüller, Globale Fehlerschätzer für Randwertprobleme mit einer Singularität zweiter Art, Technical Report, ANUM Preprint No. 6/03, Vienna University of Technology, Austria (2003).
  

• O. Koch, A. Paul, A. Traxler, E. Weinmüller, Efficient Numerical Solution of a Singular Initial Value Problem in Avalanche Modeling, Technical Report, ANUM Preprint No. 11/02, Vienna University of Technology, Austria (2002).
  

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

• W. Auzinger, G. Kneisl, O. Koch, E. B. Weinmüller, SBVP 1.0 - A MATLAB Solver for Singular Boundary Value Problems, Manual, ANUM Preprint No. 2/02, Vienna University of Technology, Austria, 2002.
  

• W. Auzinger, G. Kneisl, O. Koch, E. B. Weinmüller, A Solution Routine for Singular Boundary Value Problems, Technical Report,  ANUM Preprint No. 1/02, Vienna University of Technology, Austria, 2002.
  

• W. Auzinger, G. Kneisl, O. Koch, W. Polster, E. B. Weinmüller, Implementation of a Solution Routine for Singular Boundary Value Problems, International Seminar of ARGESIM, Working Group Simulation News, Report S70 MATLAB/SIMULINK, Vienna 2001.
  

• W. Auzinger, O. Koch, W. Polster, E.Weinmüller, Ein Algorithmus zur Gittersteuerung bei Kollokationsverfahren für singuläre Randwertprobleme, Technical Report, ANUM Preprint No. 21/01, Vienna University of Technology, Austria (2001).
  

• W. Auzinger, R. Frank, W. Kreuzer, E. B. Weinmüller,  Computergestützte Analyse verschiedener Varianten der Iterierten Defektkorrektur unter besonderen Berücksichtigung steifer Differentialgleichungen, Technical Report, ANUM Preprint No. 20/01, Vienna University of Technology, Austria, 2001
  

• W. Auzinger, R. Frank, H. Hofstätter, E. B. Weinmüller, Defektkorrektur zur numerischen Lösung steifer Anfangswertprobleme, Technical Report No. 131, Department of Applied Mathematics and Numerical Analysis, Vienna University of Technology, Vienna, Austria 2000. 
  

• W. Ruess, M. Steinböck, E. B. Weinmüller, Ein Programm zur Berechnung von Lösungen singulärer Randwertaufgaben, Manual, Department of Applied Mathematics and Numerical Analysis, Vienna University of Technology, Vienna, Austria 2000. 
  

• W. Auzinger, O. Koch, P. Kofler, E. B. Weinmüller, Acceleration Techniques for Singular IVPs,Technical Report No. 129, Department of Applied Mathematics and Numerical Analysis, Vienna University of Technology, Austria 2000, in preparation.
  

• W. Ruess, M. Steinböck, E. B. Weinmüller, Numerische Lösung singulärer Randwertaufgaben, Technical Report No. 128, Department of Applied Mathematics and Numerical Analysis, Vienna University of Technology, Vienna, Austria 1999. 
  

• W. Ruess, E. B. Weinmüller, Beschleunigte Algorithmen zur effizienten numerischen Lösung von singulären Randwertaufgaben, Technical Report No. 127, Department of Applied Mathematics and Numerical Analysis, Vienna University of Technology, Vienna, Austria 1999. 
  

• W. Auzinger, O. Koch, P. Kofler, E. B. Weinmüller, The Application of Shooting to Singular Boundary Value Problems, Technical Report No. 126, Department of Applied Mathematics and Numerical Analysis, Vienna University of Technology, Vienna, Austria 1999. 
  

• O. Koch, P. Kofler, E. B. Weinmüller, Analysis of Singular Initial and Terminal Value Problems, Technical Report No. 125, Department of Applied Mathematics and Numerical Analysis, Vienna University of Technology, Vienna, Austria 1999. 
  

• W. Auzinger, P. Kofler, E. B. Weinmüller, Steuerungsmaßnahmen bei numerischer Lösung singulärer Anfangswertprobleme, Technical Report No. 124, Department of Applied Mathematics and Numerical Analysis, Vienna University of Technology, Vienna, Austria 1999. 
  

• F. Frommlet, E. B. Weinmüller, Asymptotische Fehlerentwicklungen für singuläre Randwertaufgaben, Technical Report No. 118, Department of Applied Mathematics and Numerical Analysis, Vienna University of Technology, Vienna, Austria 1995.
  

• W. Auzinger, R. Frank, E. B. Weinmüller, On the Effizient Integration of Conservation Laws with Stiff Source Terms, Technical Report No. 94, Department of Applied Mathematics and Numerical Analysis, Vienna University of Technology, Vienna, Austria 1992.
  

• M. Gräff, E. B. Weinmüller, Schätzungen des lokalen Diskretisierungsfehlers bei singulären Randwertproblemen, Technical Report No. 66, Department of Applied Mathematics and Numerical Analysis, Vienna University of Technology, Vienna, Austria 1986.
  

• E. B. Weinmüller, A Difference Method for Nonlinear Singular Boundary Value Problems of Second Order, Technical Report No. 56, Department of Applied Mathematics and Numerical Analysis, Vienna University of Technology, Vienna, Austria 1983.
  

• E. B. Weinmüller, Erweiterung des Toronto-Modells zur Effizienzuntersuchung von numerischen Verfahren für gewöhnliche Differentialgleichungen, Doctoral Thesis, Technical Report No. 45, Department of Applied Mathematics and Numerical Analysis, Vienna University of Technology, Vienna, Austria 1980.