Numerical study of high order nonlinear dispersive PDEs using different RBF approaches

To realize and comprehend the physical phenomena of nonlinear system, exploration of traveling wave solutions plays an important role. Among the class of dispersive PDEs of traveling wave solutions the Degasperis-Procesi (DP) equation comprises high order nonlinear derivatives and is considered as a well known model for shallow water dynamics having similar asymptotic accuracy as for the Camassa-Holm (CH) equation. In this study we investigate solutions of some high order nonlinear dispersive PDEs namely generalized Degasperis-Procesi (DP), Camassa-Holm (CH) and Korteweg-de Vries (KdV) equations by the use of Radial Basis Function (RBF) combined with Finite Differences (RBF-FD) and Pseudo-Spectral (RBF-PS) methods. For the time derivative approximation, the fourth-order Runge-Kutta (RK) technique is accomplished. The efficiency and accuracy of our suggested approaches are demonstrated using examples and results.