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

    Rafal Brociek Info
    Edyta Hetmaniok Info
    Jaros law Matlak Info
    Damian Slota Info

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.

Keywords:

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

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May 19, 2016
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2016-05-19

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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

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