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Superconvergence of Legendre spectral projection methods for Fredholm–Hammerstein integral equations
, G. Nelakanti
Published in Elsevier B.V.
Volume: 319
Pages: 423 - 439
In this paper, we consider the multi-Galerkin and multi-collocation methods for solving the Fredholm–Hammerstein 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(n−3r+34) and O(n−2r+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(n−4r) and O(n−2r), respectively, in uniform norm. Numerical examples are given to illustrate the theoretical results. © 2017 Elsevier B.V.
About the journal
JournalData powered by TypesetJournal of Computational and Applied Mathematics
PublisherData powered by TypesetElsevier B.V.