Journal
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
Volume 92, Issue -, Pages 156-170Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.enganabound.2017.10.016
Keywords
Local radial basis functions (RBFs) meshless method; Differential quadrature technique; Schrodinger/Gross-Pitaevskii equation; Klein-Gordon-Zalcharov equation; Fourth-order Runge-Kutta method; Optic and laser engineering
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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 Schrodinger/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. (C) 2017 Elsevier Ltd. All rights reserved.
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