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

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 equations
• quadratic B-spline finite-element method
• semi-discrete scheme
• conservation properties

2000 AMS Subject Classifications :

• 35Q55
• 65M60
• 65N30