Analysis of new conservative difference scheme for two-dimensional Rosenau-RLW equation. Issue 7 (19th May 2017)

• Record Type: Journal Article
• Authors: Ghiloufi, Ahlem; Kadri, Tlili
• Is Part Of: Applicable analysis. Volume 96:Issue 7(2017)
• Page Start: 1255
• Page End: 1267
• Publication Date: 2017-05-19
• Subjects: Rosenau-RLW equation -- conservation -- existence -- uniqueness -- stability -- convergence; 65 M10 -- 65 M12 -- 65 M15; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2016.1186270
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : In this article, numerical solution for the Rosenau-RLW equation in 2D is considered and a conservative Crank–Nicolson finite difference scheme is proposed. Existence of the numerical solutions for the difference scheme has been shown by Browder fixed point theorem. A priori bound and uniqueness as well as conservation of discrete mass and discrete energy for the finite difference solutions are discussed. Unconditional stability and a second-order accuracy on both space and time of the difference scheme are proved. Numerical experiments are given to support our theoretical results.