Analysis of a compact multi-step ADI method for linear parabolic equation. (2nd January 2020)

• Record Type: Journal Article
• Authors: Deng, Dingwen; Wu, Qiang
• Is Part Of: International journal of modelling & simulation. Volume 40:Number 1(2020)
• Page Start: 1
• Page End: 16
• Publication Date: 2020-01-02
• Subjects: Parabolic equation -- compact ADI method -- convergence -- solvability -- Richardson extrapolation algorithm; Mathematical models -- Periodicals; Simulation methods -- Periodicals; Mathematical models; Simulation methods; Periodicals; 003.3
• DOI: 10.1080/02286203.2018.1510206
• Languages: English
• ISSNs: 0228-6203

Abstract

ABSTRACT: As we know, second-order backward differentiation formula (BDF2) is L-stable scheme, which can damp unwanted finite oscillations, while Crank-Nicolson (C-N) method is only A-stable scheme and usually causes numerical oscillations. Thus, BDF2 may be more popular than C-N. However, up to now, most of studies focus on the error analysis of the compact alternating direction implicit (ADI) method on the basis of C-N method for temporal discretization in L ∞ -norm. This paper is devoted to the convergence analysis of a compact multi-step ADI method used to solve a two-dimensional (2D) parabolic equation in L 2 -, H 1 - and L ∞ -norms. Besides, the existence of the ADI solution is also analyzed in detail. A class of Richardson extrapolation algorithms are established to improve computational efficiency. By introducing a transformation, our algorithms are easily generalized to the solution of convection-diffusion problems with constant coefficients. Numerical results confirm the performance of our algorithms and support theoretical analysis.