A METHOD TO ESTIMATE THE SOLUTION OF A WEAKLY SINGULAR NON-LINEAR INTEGRO-DIFFERENTIAL EQUATIONS BY APPLYING THE HOMOTOPY METHODS

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SADIGH BEHZADI SH.; YILDIRIM A.

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Journal: INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS Year:2012 | Volume:4 | Issue:1 Page(s): 41-51

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Title

A METHOD TO ESTIMATE THE SOLUTION OF A WEAKLY SINGULAR NON-LINEAR INTEGRO-DIFFERENTIAL EQUATIONS BY APPLYING THE HOMOTOPY METHODS

Author(s)

SADIGH BEHZADI SH. | YILDIRIM A. | Issue Writer Certificate

Keywords

VOLTERRA INTEGRAL EQUATIONS

INTEGRO-DIFFERENTIAL EQUATIONS

SINGULAR INTEGRAL EQUATIONS

HOMOTOPY ANALYSIS METHOD (HAM)

HOMOTOPY PERTURBATION METHOD (HPM)

Abstract

In this paper, the weakly singular nonlinear integro-differential equation is solved by using the homotopy perturbation and homotopy analysis methods. The approximation solution of this equation is calculated in the form of a series which its components are computed easily. The existence and uniqueness of the solution and the convergence of the proposed method are proved. A numerical example is studied to demonstrate the accuracy of the presented method.

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APA: Copy

SADIGH BEHZADI, SH., & YILDIRIM, A.. (2012). A METHOD TO ESTIMATE THE SOLUTION OF A WEAKLY SINGULAR NON-LINEAR INTEGRO-DIFFERENTIAL EQUATIONS BY APPLYING THE HOMOTOPY METHODS. INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS, 4(1), 41-51. SID. https://sid.ir/paper/600909/en

Vancouver: Copy

SADIGH BEHZADI SH., YILDIRIM A.. A METHOD TO ESTIMATE THE SOLUTION OF A WEAKLY SINGULAR NON-LINEAR INTEGRO-DIFFERENTIAL EQUATIONS BY APPLYING THE HOMOTOPY METHODS. INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS[Internet]. 2012;4(1):41-51. Available from: https://sid.ir/paper/600909/en

IEEE: Copy

SH. SADIGH BEHZADI, and A. YILDIRIM, “A METHOD TO ESTIMATE THE SOLUTION OF A WEAKLY SINGULAR NON-LINEAR INTEGRO-DIFFERENTIAL EQUATIONS BY APPLYING THE HOMOTOPY METHODS,” INTERNATIONAL JOURNAL OF INDUSTRIAL MATHEMATICS, vol. 4, no. 1, pp. 41–51, 2012, [Online]. Available: https://sid.ir/paper/600909/en

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