Application of the Homotopy Analysis Method for Solving the Systems of Linear and Nonlinear Integral Equations. Issue 3 (3rd May 2016)

• Record Type: Journal Article
• Authors: Brociek, Rafał; Hetmaniok, Edyta; Matlak, Jarosław; Słota, Damian
• Is Part Of: Mathematical modelling and analysis. Volume 21:Issue 3(2016)
• Page Start: 350
• Page End: 370
• Publication Date: 2016-05-03
• Subjects: homotopy analysis method -- convergence -- error estimation -- system of Fredholm integral equations -- system of Volterra integral equations; 65R20 -- 45F05; Mathematical models -- Periodicals; Mathematical models -- Study and teaching -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis -- Problems, exercises, etc -- Periodicals; Mathematical analysis; Mathematical models; Mathematical models -- Study and teaching; Periodicals; Problems and exercises; 511.805
• DOI: 10.3846/13926292.2016.1167787
• Languages: English
• ISSNs: 1392-6292

Abstract

Abstract: I n 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.