Legendre superconvergent Galerkin-collocation type methods for Hammerstein equations

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Abstract

In this paper, polynomially based superconvergent projection methods for approximating the solution of Hammerstein equations with a smooth kernel are studied. The projection is chosen to be either the orthogonal projection or an interpolatory projection using Legendre polynomial bases. The paper is motivated by the results reported in Nelakanti and Mandal (2017)[19]. The order of convergence of the proposed methods and those of superconvergence of the iterated versions are analyzed. Numerical example is given to illustrate the theoretical results.

Keywords

Hammerstein equation
Orthogonal projection
Interpolatory projection
Legendre polynomial
Superconvergence

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Research supported by URAC-05 .