A Lumped Galerkin finite element method for the generalized Hirota-Satsuma coupled KdV and coupled MKdV equations
N. M. Yagmurlu, B. Karaagac, A. Esen
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.
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