Solving the Generalized Rosenau-KdV Equation by the Meshless Kernel-Based Method of Lines

Abstract

This current investigation consists of the numerical solutions of the Generalized Rosenau-KdV equation by using the meshless kernel-based method of lines, which is a truly meshless method. The governing equation is a nonlinear partial differential equation but the use of the method of lines leads to an ordinary differential equation. Thus, the partial differential equation is replaced by the ordinary differential equation. The numerical efficiency of the used technique is tested by different numerical examples. Numerical values of error norms and physical invariants are compared with known values in the literature. Moreover, Multiquadric, Gaussian, and Wendland’s compactly supported functions are used in computations. It is seen that the used truly meshless method in computations is very effective with high accuracy and reliability.