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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:370

Article

Mandal, Moumita¹  Kant, Kapil²  Nelakanti, Gnaneshwar² 

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

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

关键词: Boundary value problem;    Hammerstein integral equation;    Galerkin method;    Green's function;    Piecewise polynomials;    Superconvergence rates;   

DOI  :  10.1016/j.cam.2019.112599

来源: Elsevier

【 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.

【 授权许可】

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