Legendre Spectral Projection Methods for Fredholm–Hammerstein Integral Equations

被引：0
作者：
Payel Das
Mitali Madhumita Sahani
Gnaneshwar Nelakanti
Guangqing Long
机构：
[1] Indian Institute of Technology,Department of Mathematics
[2] KIIT University,Department of Mathematics, School of Applied Sciences
[3] GuangXi Teachers Education University,Department of Mathematics
来源：
Journal of Scientific Computing | 2016年 / 68卷
关键词：
Hammerstein integral equations; Smooth kernels; Spectral method; Galerkin method; Collocation method; Legendre polynomials; Superconvergence rates;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we consider the Legendre spectral Galerkin and Legendre spectral collocation methods to approximate the solution of Hammerstein integral equation. The convergence of the approximate solutions to the actual solution is discussed and the rates of convergence are obtained. We are able to obtain similar superconvergence rates for the iterated Legendre Galerkin solution for Hammerstein integral equations with smooth kernel as in the case of piecewise polynomial based Galerkin method.
引用
收藏
页码：213 / 230
页数：17
相关论文
共 34 条
[1]  
Atkinson K(1992)A survey of numerical methods for solving nonlinear integral equations J. Integral Equ. Appl. 4 15-46
[2]  
Chen Z(2009)Fast multilevel augmentation methods for solving Hammerstein equations SIAM J. Numer. Anal. 47 2321-2346
[3]  
Bin W(2011)A fast multiscale solver for modified Hammerstein equations Appl. Math. Comput. 218 3057-3067
[4]  
Yuesheng X(1992)Numerical solutions for weakly singular Hammerstein equations and their superconvergence J. Integral Equ. Appl. 4 391-407
[5]  
Chen Z(1996)Superconvergence of the iterated Galerkin methods for Hammerstein equations SIAM J. Numer. Anal. 33 1048-1064
[6]  
Li J(1997)Superconvergence of the iterated collocation methods for Hammerstein equations J. Comput. Appl. Math. 80 335-349
[7]  
Zhang Y(1987)A new collocation-type method for Hammerstein equations Math. Comput. 48 585-593
[8]  
Kaneko H(1987)Superconvergence of a collocation-type method for Hammerstein equations IMA J. Numer. Anal. 7 313-325
[9]  
Noren RD(1990)The numerical solution of Hammerstein equations by a method based on polynomial collocation J. Aust. Math. Soc. Ser. B 31 319-329
[10]  
Xu Y(2009)Polynomially based multi-projection methods for Fredholm integral equations of the second kind Appl. Math. Comput. 215 147-155
1234