Solution of multi-dimensional Klein-Gordon-Zakharov and Schrödinger/Gross-Pitaevskii equations via local Radial Basis Functions-Differential Quadrature (RBF-DQ) technique on non-rectangular computational domains

In the current investigation, we develop an efficient truly meshless technique for solving two models in optic and laser engineering i.e. Klein-Gordon-Zakharov and Schrödinger/Gross-Pitaevskii equations in one- two- and three-dimensional cases. The employed meshless is the upwind local radial basis functions-differential quadrature (LRBF-DQ) technique. The spacial direction is discretized using the LRBF-DQ method and also to obtain high-order numerical results, the fourth-order exponential time differencing Runge-Kutta method (ETDRK4) planned by Liang et al. [37] is applied to discrete the temporal direction. To show the efficiency of the proposed method, we solve the mentioned models on some complex shaped domains. Moreover, several examples are given and simulation results show the acceptable accuracy and efficiency of the proposed scheme.