A time and space parallel algorithm for the heat equation: The implicit collocation method

  • Fabienne Jézéquel
Workshop 07 Parallel Numerical Algorithms
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1124)


A collocation method used as a parallel method across time is proposed for solving parabolic partial differential equations. With this method, the solution of the heat equation is approximated by polynomials, the coefficients of which are computed from a block-tridiagonal linear system. Once the polynomials have been determined for a given time interval, the solution can be computed in parallel at any point of this interval. If the number of points where the solution is computed in the considered time interval is sufficient, it appears that the performances of the implicit collocation method on a parallel machine are better than those of finite difference methods. Numerical experiments on a SIMD architecture are reported.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Fabienne Jézéquel
    • 1
  1. 1.Laboratoire MASI-IBP, URA-818 du CNRSUniversité Pierre et Marie CurieParis Cedex 05France

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