A meshless scaling iterative algorithm based on compactly supported radial basis functions for the numerical solution of Lane-Emden-Fowler equation

作者：Shen Quan^*

来源：Numerical Methods for Partial Differential Equations, 2012, 28(2): 554-572.

DOI：10.1002/num.20635

• compactly supported radial basis functions
• meshless collocation method
• scaling iterative algorithm

In this article, we combine the compactly supported radial basis 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 Omega subset of 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.

• 出版日期2012-3
• 单位北京大学