Stability and Convergence of a Generalized Crank-Nicolson Scheme on a Variable Mesh for the Heat Equation.

Abstract

In a previous paper devoted to the numerical solution of the Stefan problem , the author has proposed a numerical scheme to solve the heat equation on a variable mesh; this scheme is a generalization of the classical Crank-Nicolson scheme since it is identical to the Crank-Nicolson scheme in the particular case of a fixed mesh. Numerical experiments have been performed in one and two space-dimensions, but no mathematical results had been proved. In the present paper, the stability and convergence of the scheme and established together with an error estimate. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1979
Accession Number
ADA077130

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  • Pierre Jamet

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  • University of Wisconsin–Madison

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