Numerical analysis for a conservative difference scheme to solve the Schrödinger–Boussinesq equation

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• 作者：Luming Zhang^a ; ^{zhanglm@nuaa.edu.cn"" rel=""nofollow} ; Dongmei Bai^b ; Shanshan Wang^a
• 关键词：Schr&#xf6 ; dinger– ; Boussinesq equation ; Conservative difference scheme ; Existence of solution ; A priori estimates ; Numerical analysis
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2011
• 出版时间：1 July 2011
• 年：2011
• 卷：235
• 期：17
• 页码：4899-4915
• 全文大小：317 K

文摘

In this paper, we present a finite difference scheme for the solution of an initial-boundary value problem of the Schrödinger–Boussinesq equation. The scheme is fully implicit and conserves two invariable quantities of the system. We investigate the existence of the solution for the scheme, give computational process for the numerical solution and prove convergence of iteration method by which a nonlinear algebra system for unknown Vⁿ⁺¹ is solved. On the basis of a priori estimates for a numerical solution, the uniqueness, convergence and stability for the difference solution is discussed. Numerical experiments verify the accuracy of our method.