A quartic subdomain finite element method for the modified KdV equation

Abstract

In this article, we have obtained numerical solutions of the modified Korteweg-de Vries (MKdV) equation by a numerical technique attributed on subdomain finite element method using quartic B-splines. The proposed numerical algorithm is controlled by applying three test problems including single solitary wave, interaction of two and three solitary waves. To inspect the performance of the newly applied method, the error norms, L2 and L∞, as well as the four lowest invariants, I1, I2; I3 and I4 have been computed. Linear stability analysis of the algorithm is also examined.