# Homotopy approach for solving two-dimensional integral equations of the second kind

### Abstract

In this paper, the two-dimensional linear and nonlinear integral equations of the second kind is analyzed. The homotopy analysis method (HAM) is used for determining the solution of the investigated equation. In this method, a solution is sought in the series form. It is shown that if this series is convergent, its sum gives the solution of the considered equation. The sufficient condition for the convergence of the series is also presented. Additionally, the error of approximate solution, obtained as partial sum of the series, is estimated. Application of the HAM is illustrated by examples.

### Keywords

homotopy analysis method, convergence, error estimation, nonlinear integral equation, linear integral equation,### References

Published

Jan 25, 2017

How to Cite

HETMANIOK, Edyta et al.
Homotopy approach for solving two-dimensional integral equations of the second kind.

**Computer Assisted Methods in Engineering and Science**, [S.l.], v. 23, n. 1, p. 19-41, jan. 2017. ISSN 2299-3649. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/4>. Date accessed: 26 jan. 2022.
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