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

共 50 条

[41] Approximate Solution of Two-Point Boundary Value Problems Using Adomian Decomposition Method with Green's Function
Singh, Randhir
Nelakanti, Gnaneshwar
Kumar, Jitendra
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES INDIA SECTION A-PHYSICAL SCIENCES, 2015, 85 (01) : 51 - 61
[42] Approximate Solution of Two-Point Boundary Value Problems Using Adomian Decomposition Method with Green’s Function
Randhir Singh
Gnaneshwar Nelakanti
Jitendra Kumar
Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 2015, 85 : 51 - 61
[43] AUTOMATION OF SOLUTION FOR MATHEMATICAL PHYSICS BOUNDARY-VALUE PROBLEMS BY NET METHOD
KARPOV, VV
DOPOVIDI AKADEMII NAUK UKRAINSKOI RSR SERIYA A-FIZIKO-MATEMATICHNI TA TECHNICHNI NAUKI, 1978, (11): : 1017 - 1020
[44] A fixed-point theorem for S-type operators on Banach spaces and its applications to boundary-value problems
Dix, Julio G.
Karakostas, George L.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (09) : 3872 - 3880
[45] Green's function homotopy perturbation method for the initial-boundary value problems
Sawangtong, Wannika
Sawangtong, Panumart
ADVANCES IN DIFFERENCE EQUATIONS, 2019, 2019 (01)
[46] Green’s function homotopy perturbation method for the initial-boundary value problems
Wannika Sawangtong
Panumart Sawangtong
Advances in Difference Equations, 2019
[47] Fixed point iterations for a class of nonstandard Sturm-Liouville boundary value problems
Junghanns, P.
Themistoclakis, W.
Vecchio, A.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2014, 94 : 217 - 230
[48] On Numerov's method for a class of strongly nonlinear two-point boundary value problems
Wang, Yuan-Ming
APPLIED NUMERICAL MATHEMATICS, 2011, 61 (01) : 38 - 52
[49] Solving boundary value problems of mathematical physics using radial basis function networks
V. I. Gorbachenko
M. V. Zhukov
Computational Mathematics and Mathematical Physics, 2017, 57 : 145 - 155
[50] Solving boundary value problems of mathematical physics using radial basis function networks
Gorbachenko, V. I.
Zhukov, M. V.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2017, 57 (01) : 145 - 155

← 1 2 3 4 5 →