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Finding a good shape parameter of RBF to solve PDEs based on the particle swarm optimization algorithm

发现 RBF 的一个好形状参数基于粒子群优化算法解决 PDE

作     者:Koupaei, Javad Alikhani Firouznia, Marjan Hosseini, Seyed Mohammad Mahdi 

作者机构:Payame Noor Univ Dept Math Box 19395-3697 Tehran Iran Univ Khansar Dept Comp Engn Khansar Iran Shahid Bahonar Univ Kerman Dept Appl Math Kerman Iran 

出 版 物:《ALEXANDRIA ENGINEERING JOURNAL》 (亚历山大工程杂志)

年 卷 期:2018年第57卷第4期

页      面:3641-3652页

核心收录:

学科分类:12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 08[工学] 

主  题:Particle swarm optimization algorithm RBF Kansa's method PDEs Evolutionary algorithm 

摘      要:The present study aims at integrating the Particle Swarm Optimization (PSO) algorithm with Kansa s method based on meshless collocation methods in order to determine a good shape parameter of Radial Basis Function (RBF) for solving partial differential equations (PDEs). For this purpose, we use a two-staged experimental design. While in the first stage, PSO algorithm was used to determine an optimal shape parameter for the related RBFs, in the second stage, we employed Kansa s method to estimate the RMS error for specifying approximate solutions. To study the performance of the proposed algorithm, we offer numerical results for two examples of partial differential equations and show the effectiveness of the proposed method. Numerical results demonstrated the performance superiority of the new algorithm model. The findings also indicated that the evolutionary algorithm model is more effective than the golden section search algorithm in finding a good shape parameter of RBF. (C) 2018 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://***/licenses/by-nc-nd/4.0/).

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