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A lumped Galerkin finite element method for the generalized Hirota-Satsuma coupled KdV and coupled MKdV equations. (English) Zbl 1434.65284
Summary: In the present study, a Lumped Galerkin finite element method using quadratic B-splines has been applied to the generalized Hirota-Satsuma coupled Korteweg de Vries (KdV) and coupled modified Korteweg-de Vries (mKdV) equations. The numerical solutions of discretized equations using Lumped Galerkin finite element method have been obtained using the fourth order Runge-Kutta method which is widely used for the solution of ordinary differential equation system. The numerical solutions obtained for various space and time values have been compared with exact ones using the error norms \(L_2\) and \(L_{\infty}\). Lumped Galerkin finite element method is an effective one which can be applied to a wide range of nonlinear evolution equations.
MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65D07 Numerical computation using splines
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
35Q53 KdV equations (Korteweg-de Vries equations)
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