A CCD-ADI method for two-dimensional linear and nonlinear hyperbolic telegraph equations with variable coefficients. Issue 5 (4th May 2019)

• Record Type: Journal Article
• Authors: Chen, Buyun; He, Dongdong; Pan, Kejia
• Is Part Of: International journal of computer mathematics. Volume 96:Issue 5(2019)
• Page Start: 992
• Page End: 1004
• Publication Date: 2019-05-04
• Subjects: Hyperbolic telegraph equation -- combined compact difference scheme -- alternating direction implicit method -- unconditional stability -- variable coefficients; 65M06; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2018.1478415
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: In this paper, a combined compact finite difference method (CCD) together with alternating direction implicit (ADI) scheme is developed for two-dimensional linear and nonlinear hyperbolic telegraph equations with variable coefficients. The proposed CCD-ADI method is second-order accurate in time variable and sixth-order accurate in space variable. For the linear hyperbolic equation, the CCD-ADI method is shown to be unconditionally stable by using the Von Neumann stability analysis. Numerical results for both linear and nonlinear hyperbolic equations are presented to illustrate the high accuracy of the proposed method.