Abstract:
In this article, modi ed Korteweg-de Vries (mKdV) equation is solved
numerically by using lumped Petrov-Galerkin approach, where weight functions are
quadratic and the element shape functions are cubic B-splines. The proposed numerical
scheme is tested by applying four test problems including single solitary wave, interaction of two and three solitary waves, and evolution of solitons with the Gaussian initial condition.
In order to show the performance of the algorithm, the error norms, L2, L1, and a
couple of conserved quantities are computed. For the linear stability analysis of numerical
algorithm, Fourier method is also investigated. As a result, the computed results show that
the presented numerical scheme is a successful numerical technique for solving the mKdV equation. Therefore, the presented method is preferable to some recent numerical methods.
