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Numerical simulation of two‐dimensional and three‐dimensional generalized Klein–Gordon–Zakharov equations with power law nonlinearity via a meshless collocation method based on barycentric rational interpolation

This study presents numerical simulations of generalized two‐dimensional (2D) and three‐dimensional (3D) Klein–Gordon–Zakharov (KGZ) equations with power law nonlinearity, which are coupled nonlinear partial differential equations. A meshless collocation method based on barycentric rational interpolation is developed for space variable of the KGZ equations. For time discretization, an explicit low storage fourth order Runge Kutta method is proposed after transforming KGZ equations to system of ordinary differential equations by introducing auxiliary variables. L∞ and L2 error norms for some test problems are computed. Obtained numerical results and comparisons with finite element methods indicate that barycentric rational interpolation method is an efficient method for solving multidimensional generalized KGZ system numerically.