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New Techniques in Designing Finite Difference Domain Decomposition Algorithm for the Heat Equation

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Computational Science and Its Applications – ICCSA 2004 (ICCSA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3046))

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Abstract

This paper presents a new technique in designing the finite difference domain decomposition algorithm for the heat-equation. The basic procedure is to define the finite difference schemes at the interface grid points with smaller time step \(\Delta\overline{t}=\Delta{t}/m\) (m is a positive integer) by the classical explicit scheme. The stability region of the algorithm is expanded m times comparing with the classical explicit scheme, and the prior error estimates for the numerical solutions are obtained for some algorithms when m=2 or m=3. Numerical experiments on stability and accuracy are also presented.

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References

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Author information

Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, P.O. Box 8009-14, Beijing, China

    Shen Weidong & Yang Shulin

Authors
  1. Shen Weidong
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  2. Yang Shulin
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Editor information

Editors and Affiliations

  1. Department of Chemistry, University of Perugia, Via Elce di Sotto, 8, I-06123, Perugia, Italy

    Antonio Laganá

  2. Department of Computer Science, University of Calgary, 2500 University Drive N.W., T2N 1N4, Calgary, AB, Canada

    Marina L. Gavrilova

  3. William Norris Professor, Head of the Computer Science and Engineering Department, University of Minnesota, USA

    Vipin Kumar

  4. School of Computing, Soongsil University, Seoul, Korea

    Youngsong Mun

  5. OptimaNumerics Ltd., Cathedral House, 23-31 Waring Street, BT1 2DX, Belfast, UK

    C. J. Kenneth Tan

  6. Department of Mathematics and Computer Science, University of Perugia, via Vanvitelli, 1, I-06123, Perugia, Italy

    Osvaldo Gervasi

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© 2004 Springer-Verlag Berlin Heidelberg

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Weidong, S., Shulin, Y. (2004). New Techniques in Designing Finite Difference Domain Decomposition Algorithm for the Heat Equation. In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds) Computational Science and Its Applications – ICCSA 2004. ICCSA 2004. Lecture Notes in Computer Science, vol 3046. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24768-5_1

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  • DOI: https://doi.org/10.1007/978-3-540-24768-5_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-22060-2

  • Online ISBN: 978-3-540-24768-5

  • eBook Packages: Springer Book Archive

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