A Hybrid Semi-Analytical Method with Natural Transform for Solving Integro-Differential Equations

George. A. Toma¹

Section:Research Paper, Product Type: Journal-Paper
Vol.7 , Issue.3 , pp.1-7, Jun-2020

Online published on Jun 30, 2020

Copyright © George. A. Toma . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper article, we proposed a new hybrid method to find analytical approximate or exact solutions for various many linear and nonlinear integro ? differential equations. This proposed hybrid method combines a semi-analytical method which is the homotopy perturbation method with the natural transform for solving initial value problems represented by linear and non-linear integro - differential equations of the first order. The basic steps of the proposed hybrid scheme are deriving the integro - differential equation twice so we got two additional initial conditions, then we applied the natural transform to the obtained equation that we got after the derivation, thus this equation has been converted to a new equation containing Natural transform variables and ,based on it, we constructed the Homotopy. We presented three problems to test the accuracy and effectiveness of the proposed hybrid technique, our numerical results were also compared with the exact solutions. The new proposed technique method is simple, effective and fast power, simplicity and efficiency.

Key-Words / Index Term :
Homotopy Perturbation Method, Initial Value Problems , Linear and Nonlinear Integro-Differential Equations, Natural Transform.

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