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

被引：36
作者：
Dehghan, Mehdi [1 ]
Abbaszadeh, Mostafa [1 ]
机构：
[1] Amirkabir Univ Technol, Fac Math & Comp Sci, Dept Appl Math, 424 Hafez Ave, Tehran 15914, Iran
来源：
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2018年 / 92卷
关键词：
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; PROBABILITY DENSITY-FUNCTION; SOLITARY WAVE SOLUTION; JUMP-DIFFUSION MODELS; NUMERICAL-SOLUTION; FD METHOD; PSEUDOSPECTRAL METHOD; SHAPE PARAMETER; SYSTEM; APPROXIMATION; ELASTOPLASTICITY;
D O I：
10.1016/j.enganabound.2017.10.016
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
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.
引用
收藏
页码：156 / 170
页数：15
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