Numerical solutions of the mrlw equation using moving least square collocation method

Abstract

In this paper, the Modified Regularized Long Wave (MRLW) equation is solved by using moving least square collocation (MLSC) method. To show the accuracy of the used method several numerical test examples are given. The motion of single solitary waves, the interaction of two solitary waves and the Maxwellian initial condition problems are chosen as test problems. For the single solitary wave motion whose analytical solution is known L-2, L-infinity error norms are calculated. Also mass, energy and momentum invariants are calculated for every test problem. Obtained numerical results are compared with some earlier works. According to the obtained results, the method is very efficient and reliable.