Numerical solution of a coupled modified Korteweg–de Vries equation by the Galerkin method using quadratic B-splines

Abstract

In this paper, numerical solutions of a coupled modified Korteweg–de Vries equation have been obtained by the quadratic B-spline Galerkin finite element method. The accuracy of the method has been demonstrated by five test problems. The obtained numerical results are found to be in good agreement with the exact solutions. A Fourier stability analysis of the method is also investigated.

Keywords:

• coupled mKdV equation
• finite element method
• Galerkin method
• quadratic B-spline
• Fourier stability analysis

2010 AMS Subject Classifications:

• 65D07
• 65N30
• 74S05
• 65L60