Convergence analysis for derivative dependent Fredholm-Hammerstein integral equations with Green's kernel

被引：8

作者：

Mandal, Moumita ^{[1
]}

Kant, Kapil ^{[2
]}

Nelakanti, Gnaneshwar ^{[2
]}

机构：

[1] Indian Inst Technol Jodhpur, Dept Math, Jodhpur 342037, Rajasthan, India

[2] Indian Inst Technol Kharagpur, Dept Math, Kharagpur 721302, W Bengal, India

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2020年 / 370卷

关键词：

Boundary value problem; Hammerstein integral equation; Galerkin method; Green's function; Piecewise polynomials; Superconvergence rates; SPECTRAL PROJECTION METHODS; BOUNDARY-VALUE-PROBLEMS; COLLOCATION-TYPE METHOD; DIFFUSION-PROBLEMS; SUPERCONVERGENCE;

D O I：

10.1016/j.cam.2019.112599

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we consider a class of derivative dependent Fredholm-Hammerstein integral equations i.e., the integral equation, where the nonlinear function inside the integral sign is dependent on derivative and the kernel function is of Green's type. We propose the piecewise polynomial based Galerkin and iterated Galerkin methods to solve these type of derivative dependent Fredholm-Hammerstein integral equations. We discuss the convergence and error analysis of the proposed methods and also obtain the superconvergence results for iterated Galerkin approximations. Some numerical results are given to illustrate this improvement. (C) 2019 Elsevier B.V. All rights reserved.

引用

页数：16

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