High Order Energy-Preserving Method of the "Good" Boussinesq Equation. Issue 1 (15th February 2016)

• Record Type: Journal Article
• Authors: Jiang, Chaolong; Sun, Jianqiang; He, Xunfeng; Zhou, Lanlan
• Is Part Of: Numerical mathematics. Volume 9:Issue 1(2016)
• Page Start: 111
• Page End: 122
• Publication Date: 2016-02-15
• Subjects: 65D17; "Good" Boussinesq equation, -- average vector field method, -- solitary waves, -- conservation law; Numerical analysis -- Periodicals; Numerical analysis; Periodicals; 518.05
• DOI: 10.4208/nmtma.2015.m1420
• Languages: English
• ISSNs: 1004-8979

Abstract

Abstract: The fourth order average vector field (AVF) method is applied to solve the "Good" Boussinesq equation. The semi-discrete system of the "good" Boussinesq equation obtained by the pseudo-spectral method in spatial variable, which is a classical finite dimensional Hamiltonian system, is discretizated by the fourth order average vector field method. Thus, a new high order energy conservation scheme of the "good" Boussinesq equation is obtained. Numerical experiments confirm that the new high order scheme can preserve the discrete energy of the "good" Boussinesq equation exactly and simulate evolution of different solitary waves well.