Taylor-Series Expansion Methods for Multivariate Hammerstein Integral Equations

A new Taylor-series method which was originally developed for the solution of one-dimensional integral equations is extended to solve multivariate nonlinear integral equations. In this paper, a new method is constructed to approximate the solutions of a class of multivariate Hammerstein equations. O...

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Published in:IAENG international journal of applied mathematics 2017-11, Vol.47 (4), p.1-5
Main Authors: Neamprem, Khomsan, Klangrak, Apinya, Kaneko, Hideaki
Format: Article
Language:English
Subjects:
Integral equations
Monte Carlo simulation
Multivariate analysis
Nonlinear equations
Parallel processing
Series expansion
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Klangrak, Apinya
Kaneko, Hideaki
description A new Taylor-series method which was originally developed for the solution of one-dimensional integral equations is extended to solve multivariate nonlinear integral equations. In this paper, a new method is constructed to approximate the solutions of a class of multivariate Hammerstein equations. One of the strength of the new method is that it lends itself to parallel computation. Hence it is a very highly efficient method. Another strength of the proposed method is that it also gives highly accurate approximations for all the derivatives of the solution up to the order of the Taylor-series approximation used in the method. Numerical examples are given to illustrate the efficiency and accuracy of the method.
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subjects Integral equations
Monte Carlo simulation
Multivariate analysis
Nonlinear equations
Parallel processing
Series expansion
title Taylor-Series Expansion Methods for Multivariate Hammerstein Integral Equations
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