Extrapolation algorithm of compact ADI approximation for two-dimensional parabolic equation. (English) Zbl 1309.65102
Summary: 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.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 35K20 | Initial-boundary value problems for second-order parabolic equations |
Keywords:
Richardson extrapolation algorithm; compact ADI scheme; maximum norm convergence; parabolic equationReferences:
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