Superconvergent scheme for a system of Green nonlinear Fredholm integral equations

被引：0

作者：

Kumar, Rakesh ^{[1
]}

Kumar, B. V. Rathish ^{[1
]}

机构：

[1] Indian Inst Technol Kanpur, Dept Math & Stat, Kanpur 208016, India

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2024年 / 479卷

关键词：

Fredholm integral equation; Green kernel; Galerkin method; Iterated Galerkin method; BOUNDARY-VALUE-PROBLEMS; NUMERICAL-SOLUTION; DIFFUSION-PROBLEMS;

D O I：

10.1016/j.amc.2024.128880

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This study investigates a system of second-kind nonlinear Fredholm integral equations (SSNFIEs) featuring a Green's type kernel function. To solve this integral equations (IEs), we introduce Galerkin and iterated Galerkin (IG) methods based on piecewise polynomials. Convergence and error analysis are conducted for these methods, and we demonstrate superconvergence for the IG method. Numerical tests are employed to validate the theoretical findings.

引用

页数：24

共 42 条

[1] Numerical solution of second-order, two-point boundary value problems using continuous genetic algorithms
Abo-Hammour, ZS
Yusuf, M
Mirza, NM
Mirza, SM
Arif, M
Khurshid, J
[J]. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2004, 61 (08) : 1219 - 1242
[2] Ahues M., 2001, SPECTRAL COMPUTATION
[3] ANDERSON N, 1985, B MATH BIOL, V47, P145, DOI 10.1016/S0092-8240(85)90009-6
[4] [Anonymous], 1979, Hydraulics of groundwater
[5] POINTWISE SOLUTION BOUNDS FOR A CLASS OF SINGULAR DIFFUSION-PROBLEMS IN PHYSIOLOGY
ASAITHAMBI, NS
GARNER, JB
[J]. APPLIED MATHEMATICS AND COMPUTATION, 1989, 30 (03) : 215 - 222
[6] Atkinson K., 1988, J. Integral Equ. Appl., P17
[7] Bergman T.L., 2011, Fundamentals of Heat and Mass Transfer
[8] Numerical study for a class of singular two-point boundary value problems using Green's functions
Cen, Zhongdi
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 183 (01) : 10 - 16
[9] Approximation methods for system of nonlinear Fredholm-Hammerstein integral equations
Chakraborty, Samiran
Nelakanti, Gnaneshwar
[J]. COMPUTATIONAL & APPLIED MATHEMATICS, 2021, 40 (01)
[10] Chatelin F., 2011, SPECTRAL APPROXIMATI

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