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.