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Extrapolation algorithm of compact ADI approximation for two-dimensional parabolic equation

Authors
Journal
Applied Mathematics and Computation
0096-3003
Publisher
Elsevier
Publication Date
Volume
219
Issue
6
Identifiers
DOI: 10.1016/j.amc.2012.09.006
Keywords
  • Richardson Extrapolation Algorithm
  • Compact Adi Scheme
  • Maximum Norm Convergence
  • Parabolic Equation
Disciplines
  • Computer Science

Abstract

Abstract In this paper, we propose a compact alternating direction implicit (ADI) scheme for solving the two-dimensional parabolic equation. The maximum norm convergence is proven, and the convergence rate is second-order in time and fourth-order in space. We develop a Richardson extrapolation algorithm to increase the accuracy to sixth-order both in time and space. Numerical experiments show the effectiveness of the method.

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