Numerical solutions of the integral equations: Homotopy perturbation method and Adomian’s decomposition method

• Published in: Applied mathematics and computation Vol. 173; no. 1; pp. 493 - 500
• Main Author: Abbasbandy, S.
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 01-02-2006; Elsevier
• Subjects: Adomian’s decomposition method; Exact sciences and technology; Fredholm integral equations; Homotopy perturbation method; Integral equations; Integral equations, integral transforms; Mathematical analysis; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Sciences and techniques of general use; Fredholm integral equations; Homotopy perturbation method; Adomian’s decomposition method; Numerical integration; Singular equation; Decomposition method; Iterative method; Fredholm equation; Numerical approximation; Perturbation method; Numerical analysis; Numerical solution; Homotopy; Integral equation; Adomian's decomposition method
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2005.04.077

In this paper, 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 non-singular integral equations of the first kind. The results reveal that the proposed method is very effective and simple.