An IMEX Approach Assembled with Radial Basis Function-Finite Difference (RBF-FD) Method for Numerical Solution of Zakharov–Kuznetsov Modified Equal Width (ZKMEW) Equation with Power Law Nonlinearity Arising in Wave Phenomena

This study deals with numerical solutions of Zakharov–Kuznetsov modified equal width (ZKMEW) equation with power law nonlinearity which is used in modeling of wave phenomena. The ZKMEW equation is a two-dimensional (2D) nonlinear partial differential equation and for numerical solution of it we first use an implicit–explicit (IMEX) backward differentiation formula for discretization of temporal variable and obtain a semi-discrete system. The IMEX approach treats nonlinear terms explicitly and linear terms implicitly. In this way, we avoid of solving nonlinear system of equations which is a big advantage in sense of computational load. Then space variables of the semi-discrete system are discretized via a local meshless radial basis function-finite difference (RBF-FD) method. For RBF-FD method we employ polyharmonic splines (PHS) which are free of shape parameters. One advantage of using RBF-FD method is its local property. Owing to the local property of the RBF-FD method sparse matrices are used which is an advantage in sense of execution time. Some numerical simulations are carried out and comparisons with the generalized finite difference method and space–time cloud method are performed. Stability of the proposed method is examined numerically. Obtained results verify efficiency and accuracy of the proposed method.