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Parallel Two-Step W-Methods on Singular Perturbation Problems

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Parallel Processing and Applied Mathematics (PPAM 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2328))

Abstract

Parallel two-step W-methods (shortly PTSW-methods) use s linearly-implicit external stages which may be processed in parallel. We discuss convergence properties of these methods on singularly perturbed problems and give estimates for the global error for non-constant stepsizes. Due to the high stage order of the method no order reduction occurs.

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References

  1. CWI test set for IVP solvers, http://www.cwi.nl/cwi/projects/IVPtestset.

  2. E. Hairer, Ch. Lubich, and M. Roche, The numerical solution of differential-algebraic systems by Runge-Kutta methods, LN in Mathematics 1409 (1989), Springer.

    Google Scholar 

  3. E. Hairer and G. Wanner, Stiff differential equations solved by Radau methods, J. Comput. Appl. Math. 111 (1999), 93–111.

    Article  MathSciNet  MATH  Google Scholar 

  4. -, Solving Ordinary Differential Equations II, 2. ed., Springer, 1996.

    Google Scholar 

  5. H. Podhaisky, B.A. Schmitt, and R. Weiner, Design, analysis and testing of some parallel two-step W-methods for stiff systems, to appear in APNUM.

    Google Scholar 

  6. S. Schneider, Convergence results for general linear methods on singular perturbation problems, BIT 33 (1993), 670–686.

    Article  MathSciNet  MATH  Google Scholar 

  7. R. Weiner, B.A. Schmitt, and H. Podhaisky, Two-step W-methods on singular perturbation problems, Report 73, FB Mathematik, Univ. Marburg (2000).

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik und Informatik, Universität Halle, D-06099, Halle, Germany

    R. Weiner & H. Podhaisky

  2. Fachbereich Mathematik und Informatik, Universität Marburg, D-35032, Marburg, Germany

    B. A. Schmitt

Authors
  1. R. Weiner
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  2. B. A. Schmitt
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  3. H. Podhaisky
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Editor information

Editors and Affiliations

  1. Institute of Mathematics and Computer Science, Technical University of Czestochowa, Dabrowskiego 73, 42-200, Czestochowa, Poland

    Roman Wyrzykowski

  2. Computer Science Department, University of Tennessee, 122 Volunteer Blvd, Knoxville, TN, 37996-3450, USA

    Jack Dongarra

  3. Computer Science Department, Oklahoma State University, 700 N. Greenwood Ave., Tulsa, OK, 74106, USA

    Marcin Paprzycki

  4. DTU, UNI-C, Danish Computing Centre for Research and Education, Bldg. 304, 2800, Lyngby, Denmark

    Jerzy Waśniewski

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© 2002 Springer-Verlag Berlin Heidelberg

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Weiner, R., Schmitt, B.A., Podhaisky, H. (2002). Parallel Two-Step W-Methods on Singular Perturbation Problems. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2001. Lecture Notes in Computer Science, vol 2328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48086-2_87

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  • DOI: https://doi.org/10.1007/3-540-48086-2_87

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43792-5

  • Online ISBN: 978-3-540-48086-0

  • eBook Packages: Springer Book Archive

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