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

• DOI: 10.1016/j.matcom.2014.02.007
• Publication Date: 2014-04-16T00:31:24Z
• Authors: Francisco J. Domí...; Sanzon Mendoza Ar...; G. Tinoco-Guerrero; J.G. Tinoco-Ruiz
• Keywords: Heat equation; Finite difference

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.