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Fast solution of implicit methods for linear hyperbolic equations

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  • Evans, D.J.
  • Benson, A.

Abstract

A factorisation method is described for the fast numerical solution of constant tridiagonal Toeplitz linear systems which occur repeatedly in the solution of the implicit finite difference equations derived from linear first order hyperbolic equations, i.e. the Transport equation, under a variety of boundary conditions. In this paper, we show that such special linear systems can be solved efficiently by the factorisation of the coefficient matrix into two easily inverted matrices.

Suggested Citation

  • Evans, D.J. & Benson, A., 1982. "Fast solution of implicit methods for linear hyperbolic equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 24(1), pages 49-53.
    • Handle: RePEc:eee:matcom:v:24:y:1982:i:1:p:49-53
    DOI: 10.1016/0378-4754(82)90049-0
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    References listed on IDEAS

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    1. Evans, D.J., 1979. "Direct methods of solution of partial differential equations with periodic boundary conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 21(3), pages 270-275.
    2. Benson, A. & Evans, D.J., 1979. "Iterative methods of solution for the elliptic fourth boundary value problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 21(3), pages 282-288.
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    1. Evans, D.J., 1979. "Direct methods of solution of partial differential equations with periodic boundary conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 21(3), pages 270-275.

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