Conservative compact finite difference scheme for the N‐coupled nonlinear Klein–Gordon equations. Issue 3 (11th January 2019)

• Record Type: Journal Article
• Authors: Ji, Bingquan; Zhang, Luming; Zhou, Xuanxuan
• Is Part Of: Numerical methods for partial differential equations. Volume 35:Issue 3(2019)
• Page Start: 1056
• Page End: 1079
• Publication Date: 2019-01-11
• Subjects: conservative compact finite difference scheme -- convergence -- N‐coupled nonlinear Klein–Gordon equations -- stability -- the cut‐off function technique; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22338
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : In this article, a compact finite difference method is developed for the periodic initial value problem of the N‐coupled nonlinear Klein–Gordon equations. The present scheme is proved to preserve the total energy in the discrete sense. Due to the difficulty in obtaining the priori estimate from the discrete energy conservation law, the cut‐off function technique is employed to prove the convergence, which shows the new scheme possesses second order accuracy in time and fourth order accuracy in space, respectively. Additionally, several numerical results are reported to confirm our theoretical analysis. Lastly, we apply the reliable method to simulate and study the collisions of solitary waves numerically.