Comparison between two meshless methods for the Rosenau-Kawahara equation

Abstract

In this work, we present a comparative study of meshless radial basis functions collocation method and meshless kernel based method of lines for the numerical solution of the general form of Rosenau-Kawahara equation. Traveling wave solutions are simulated by using the meshless methods with well-known radial basis functions. To test the applicability and reliability of the methods, different test problems are studied. Computed numerical values of error norms and physical conservations are presented. Simulations of waves for test problems are figured. Comparisons of obtained numerical results are shown in different tables. Comparative results show that meshless methods are very effective methods with high accuracy.