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Support-operators method for PDE discretization: symbolic algorithms and realization

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  • Liska, Richard
  • Shashkov, Mikhail Yu.
  • Solovjov, Andrey V.

Abstract

The paper deals with the development and implementation of symbolic algorithms for the support-operators method for construction of finite-difference schemes. i.e., discretization of partial differential equations (PDEs), on a nonorthogonal logically rectangular grid. The general description of the support-operators method in the framework of the symbolic manipulation approach is presented. On the base of fundamental algorithms, developed earlier, algorithms for the construction of an adjoint difference operator are designed. These algorithms play a key role in the realization of the support-operators method. The algorithms have been implemented in the computer algebra system REDUCE. A 2D example demonstrates the power of the developed symbolic computation tool.

Suggested Citation

  • Liska, Richard & Shashkov, Mikhail Yu. & Solovjov, Andrey V., 1993. "Support-operators method for PDE discretization: symbolic algorithms and realization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 35(2), pages 173-183.
    • Handle: RePEc:eee:matcom:v:35:y:1993:i:2:p:173-183
    DOI: 10.1016/0378-4754(93)90012-J
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    References listed on IDEAS

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    1. G. O. Cook, 1990. "Alpal, A Program To Generate Physics Simulation Codes From Natural Descriptions," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-51.
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