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Finite difference schemes satisfying an optimality condition for the unsteady heat equation

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  • Domínguez-Mota, Francisco J.
  • Armenta, Sanzon Mendoza
  • Tinoco-Guerrero, G.
  • Tinoco-Ruiz, J.G.

Abstract

In this paper we present a formulation of a finite difference Crank–Nicolson scheme for the numerical solution of the unsteady heat equation in 2+1 dimensions, a problem which has not been extensively studied when the spatial domain has an irregular shape. It is based on a second order difference scheme defined by an optimality condition, which has been developed to solve Poisson-like equations whose domains are approximated by structured convex grids over very irregular regions generated by the direct variational method. Numerical examples are presented and the results are very satisfactory.

Suggested Citation

  • Domínguez-Mota, Francisco J. & Armenta, Sanzon Mendoza & Tinoco-Guerrero, G. & Tinoco-Ruiz, J.G., 2014. "Finite difference schemes satisfying an optimality condition for the unsteady heat equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 106(C), pages 76-83.
    • Handle: RePEc:eee:matcom:v:106:y:2014:i:c:p:76-83
    DOI: 10.1016/j.matcom.2014.02.007
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    References listed on IDEAS

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    1. Tinoco-Ruiz, J.G. & Barrera-Sánchez, P., 1998. "Smooth and convex grid generation over general plane regions1Supported by CONACyT and U.M.S.N.H.1," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 46(2), pages 87-102.
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    Cited by:

    1. Carlos Chávez-Negrete & Daniel Santana-Quinteros & Francisco Domínguez-Mota, 2021. "A Solution of Richards’ Equation by Generalized Finite Differences for Stationary Flow in a Dam," Mathematics, MDPI, vol. 9(14), pages 1-14, July.

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