The quadratic B-spline finite-element method for the coupled Schrödinger–Boussinesq equations

Abstract

Abstract In this paper, a quadratic B-spline finite-element method is proposed for solving the coupled Schrödinger–Boussinesq equations numerically. A semi-discrete finite-element scheme is constructed for this system. The existence and uniqueness of the numerical solutions and the convergence of the discrete scheme are discussed. Numerical results indicate that the proposed method is accurate and efficient. Keywords: coupled Schrödinger–Boussinesq equationsquadratic B-spline finite-element methodsemi-discrete schemeconservation properties 2000 AMS Subject Classifications : 35Q5565M6065N30