Solving non-strongly elliptic pseudodifferential equations on a sphere using radial basis functions

被引：1

作者：

Pham, D. T. ^{[1
]}

Tran, T. ^{[2
]}

机构：

[1] Vietnamese German Univ, Binh Duong City, Binh Duong Prov, Vietnam

[2] Univ New S Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2015年 / 70卷 / 08期

基金：

澳大利亚研究理事会;

关键词：

Elliptic pseudodifferential equation; Sphere; Radial basis function; Galerkin method; Collocation method; POSITIVE-DEFINITE FUNCTIONS; COLLOCATION; CONVERGENCE;

D O I：

10.1016/j.camwa.2015.08.018

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Non-strongly elliptic pseudodifferential equations on the unit sphere arise from geodesy. An example of equations of this type is the boundary integral reformulation of a boundary value problem with the Laplace equation in the interior domain of the unit sphere, and a Robin boundary condition. Approximate solutions with spherical radial basis functions are found by the Galerkin and collocation methods. The paper presents a unified theory for error analysis of both approximation methods. The theoretical results are corroborated by numerical experiments. It is noted that the stiffness matrix arising from the Galerkin method for this problem resembles that arising from a least squares method. (C) 2015 Elsevier Ltd. All rights reserved.

引用

页码：1970 / 1983

页数：14

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