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Application of the Homotopy Analysis Method for Solving the Systems of Linear and Nonlinear Integral Equations

    Rafal Brociek Affiliation
    ; Edyta Hetmaniok Affiliation
    ; Jaros law Matlak Affiliation
    ; Damian Slota Affiliation

Abstract

In this paper we indicate some applications of homotopy analysis method for solving the systems of linear and nonlinear integral equations. The method is based on the concept of creating function series. If the series converges, its sum is the solution of this system of equations. The paper presents conditions to ensure the convergence of this series and estimation of the error of approximate solution obtained when the partial sum of the series is used. Application of the method will be illustrated by examples.

Keyword : homotopy analysis method, convergence, error estimation, system of Fredholm integral equations, system of Volterra integral equations

How to Cite
Brociek, R., Hetmaniok, E., Matlak, J. law, & Slota, D. (2016). Application of the Homotopy Analysis Method for Solving the Systems of Linear and Nonlinear Integral Equations. Mathematical Modelling and Analysis, 21(3), 350-370. https://doi.org/10.3846/13926292.2016.1167787
Published in Issue
May 19, 2016
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