Title: A high accuracy variant of the iterative alternating decomposition explicit method for solving the heat equation

Authors: M.S. Sahimi, N.A. Mansor, N.M. Nor, N.M. Nusi, N. Alias

Addresses: Department of Engineering Sciences and Mathematics, Universiti Tenaga Nasional, 43009 Kajang, Selangor, Malaysia. ' Department of Engineering Sciences and Mathematics, Universiti Tenaga Nasional, 43009 Kajang, Selangor, Malaysia. ' Department of Engineering Sciences and Mathematics, Universiti Tenaga Nasional, 43009 Kajang, Selangor, Malaysia. ' Department of Engineering Sciences and Mathematics, Universiti Tenaga Nasional, 43009 Kajang, Selangor, Malaysia. ' Department of Mathematics, Universiti Teknologi Malaysia, 81310 UTM Skudai, Johor, Malaysia

Abstract: We consider three level difference replacements of parabolic equations focusing on the heat equation in two space dimensions. Through a judicious splitting of the approximation, the scheme qualifies as an alternating direction implicit (ADI) method. Using the well known fact of the parabolic-elliptic correspondence, we shall derive a two stage iterative procedure employing a fractional splitting strategy applied alternately at each intermediate time step to the one dimensional heat equation. As the basis of derivation is the unconditionally stable (4,2) accurate ADI scheme, this method is convergent, computationally stable and highly accurate.

Keywords: alternating direction implicit method; ADI method; iterative alternating decomposition explicit method; IADE method; fractional splitting; heat equation.

DOI: 10.1504/IJSPM.2006.009011

International Journal of Simulation and Process Modelling, 2006 Vol.2 No.1/2, pp.45 - 49

Published online: 12 Feb 2006 *

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