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

• Published in: Journal of computational and applied mathematics 2011-07, Vol.235 (17), p.4899-4915
• Main Authors: Zhang, Luming, Bai, Dongmei, Wang, Shanshan
• Format: Article
• Language: English
• Subjects: A priori estimates; Algebra; Boundary value problems; Computation; Conservative difference scheme; Convergence; Exact sciences and technology; Existence of solution; Initial value problems; Mathematical analysis; Mathematical models; Mathematics; Numerical analysis; Numerical analysis in abstract spaces; Numerical analysis. Scientific computation; Partial differential equations; Partial differential equations, boundary value problems; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Schrödinger–Boussinesq equation; Sciences and techniques of general use; Uniqueness
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2011.04.001

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 V n + 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.