Homotopy Perturbation Method and Convergence Analysis for the Linear Mixed Volterra-Fredholm Integral Equations

Pakhshan Mohammed Ameen Hasan; Nejmaddin Abdulla Sulaiman

doi:10.24996/ijs.2020.61.2.19

Authors

Pakhshan Mohammed Ameen Hasan Department of Mathematics, Collage of Education, Salahddin University, Erbil, Iraq
Nejmaddin Abdulla Sulaiman Department of Mathematics, Collage of Education, Salahddin University, Erbil, Iraq

DOI:

https://doi.org/10.24996/ijs.2020.61.2.19

Keywords:

Aitken method, homotopy perturbation method, second kind linear mixed Volterra-Fredholm integral equations (LMVFIE2nd)

Abstract

In this paper, the homotopy perturbation method is presented for solving the second kind linear mixed Volterra-Fredholm integral equations. Then, Aitken method is used to accelerate the convergence. In this method, a series will be constructed whose sum is the solution of the considered integral equation. Convergence of the constructed series is discussed, and its proof is given; the error estimation is also obtained. For more illustration, the method is applied on several examples and programs, which are written in MATLAB (R2015a) to compute the results. The absolute errors are computed to clarify the efficiency of the method.