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A meshless scaling iterative algorithm based on compactly supported radial basis functions for the numerical solution of Lane‐Emden‐Fowler equation
Author(s) -
Shen Quan
Publication year - 2012
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20635
Subject(s) - mathematics , finite element method , radial basis function , collocation method , partial differential equation , collocation (remote sensing) , dirichlet boundary condition , domain (mathematical analysis) , boundary (topology) , scaling , basis function , bounded function , algorithm , orthogonal collocation , mathematical analysis , differential equation , geometry , ordinary differential equation , computer science , physics , machine learning , artificial neural network , thermodynamics
Abstract In this article, we combine the compactly supported radial basis function (RBF) collocation method and the scaling iterative algorithm to compute and visualize the multiple solutions of the Lane‐Emden‐Fowler equation on a bounded domain Ω ⊂ R 2 with a homogeneous Dirichlet boundary condition. This novel method has the advantage over traditional methods, which approximate the spatial derivatives using either the finite difference method (FDM), the finite element method (FEM), or the boundary element method (BEM), because it does not require a mesh over the domain. As a result, it needs less computational time than the globally supported RBF collocation method. When compared with the reference solutions in (Chen, Zhou, and Ni, Int J Bifurcation Chaos 10 (2000), 565–1612), our numerical results demonstrate the accuracy and ease of implementation of this method. It is therefore much more suitable for dealing with the complex domains than the FEM, the FDM, and the BEM. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 554‐572, 2012