A Class of Boundary Value Problems Arising in Mathematical Physics: A Green's Function Fixed-point Iteration Method

被引：1

作者：

Khuri, Suheil ^{[1
]}

Sayfy, Ali ^{[1
]}

机构：

[1] Amer Univ Sharjah, Dept Math & Stat, Sharjah, U Arab Emirates

来源：

ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES | 2015年 / 70卷 / 05期

关键词：

Boundary Value Problems; Fixed-Point Iteration Schemes; Green's Function; GAUSS COLLOCATION METHOD; YAMABE-EQUATION; JACOBI; APPROXIMATION; ALGORITHM;

D O I：

10.1515/zna-2014-0327

中图分类号：

O64 [物理化学（理论化学）、化学物理学];

学科分类号：

070304 ; 081704 ;

摘要：

This paper presents a method based on embedding Green's function into a well-known fixed-point iteration scheme for the numerical solution of a class of boundary value problems arising in mathematical physics and geometry, in particular the Yamabe equation on a sphere. Convergence of the numerical method is exhibited and is proved via application of the contraction principle. A selected number of cases for the parameters that appear in the equation are discussed to demonstrate and confirm the applicability, efficiency, and high accuracy of the proposed strategy. The numerical outcomes show the superiority of our scheme when compared with existing numerical solutions.

引用

页码：343 / 350

页数：8

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