Superconvergence of Legendre spectral projection methods for Fredholm–Hammerstein integral equations
| Autor: | Moumita Mandal, Gnaneshwar Nelakanti |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Legendre wavelet
Applied Mathematics Mathematical analysis 010103 numerical & computational mathematics Legendre's equation 01 natural sciences Legendre function Mathematics::Numerical Analysis 010101 applied mathematics Legendre transformation Computational Mathematics symbols.namesake Associated Legendre polynomials Legendre form symbols 0101 mathematics Legendre's constant Legendre polynomials Mathematics |
| Zdroj: | Journal of Computational and Applied Mathematics. 319:423-439 |
| ISSN: | 0377-0427 |
| DOI: | 10.1016/j.cam.2017.01.027 |
| Popis: | In this paper, we consider the multi-Galerkin and multi-collocation methods for solving the FredholmHammerstein integral equation with a smooth kernel, using Legendre polynomial bases. We show that Legendre multi-Galerkin and Legendre multi-collocation methods have order of convergence O(n3r+34) and O(n2r+12), respectively, in uniform norm, where n is the highest degree of Legendre polynomial employed in the approximation and r is the smoothness of the kernel. Also, one step of iteration method is used to improve the order of convergence and we prove that iterated Legendre multi-Galerkin and iterated Legendre multi-collocation methods have order of convergence O(n4r) and O(n2r), respectively, in uniform norm. Numerical examples are given to illustrate the theoretical results. |
| Databáze: | OpenAIRE |
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