Numerical solutions of the integral equations: homotopy perturbation method and Adomian’s decomposition method. (English) Zbl 1090.65143

Abbasbandy, S.

Appl. Math. Comput. 173, No. 1, 493-500 (2006).

Summary: A homotopy perturbation method is proposed to solve non-singular integral equations. Comparisons are made between Adomian’s decomposition method and the proposed method. It is shown, Adomian’s decomposition method is a homotopy, only. Finally, by using homotopy perturbation method, a new iterative scheme, like Adomian’s decomposition method, is proposed for solving the nonsingular integral equations of the first kind. The results reveal that the proposed method is very effective and simple.

MSC:

65R20	Numerical methods for integral equations
45B05	Fredholm integral equations

Keywords:

homotopy perturbation method; Fredholm integral equations; Adomian’s decomposition method; numerical examples; comparison of methods

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