SOLUTION OF FREDHOLM INTEGRO-DIFFERENTIAL EQUATION BY VARIATIONAL ITERATION METHOD

Authors

Keywords:

Variational Iteration Method, Fredholm integro-differential, Equation Initial Approximation, Numerical Solution

Abstract

The Variational Iteration Method is applied to solve Fredholm Integro-differential Equation. The initial approximation was selected wisely which satisfies the initial condition of the given Fredholm Integro-differential Equation. The numerical result was analyzed with the aid of Mat-Lab and Maple software’s and are compared with the exact solution to show the usefulness and efficiency of the Method. The results show that the Variational Iteration Method is very efficient, reliable and of high accuracy for solving Fredholm Integro-differential Equation when compared with the exact solution.

Dimensions

Abbasbandy S. and Shivanian E. (2009). Application of the Variational Iteration Method for system of nonlinear Volterra Integro-differential equations. Mathematical and Computational Applications vol. 14, No. 2, 147- 158.

Abdou M.A. and Soliman A.A. (2005). Variational Iteration Method for solving Buger’s equations. Journal of Computational and Applied Mathematics 181, 245-251.

An Iterative method for solving fourth-order boundary value problems of mixed type Integro-differential equation. Journal of computational Analytic and Applications. 1-18

Al-Khaled, K. (2005). The decomposition method of solving nonlinear IDEs. Appl. Math and Comp. 165(2), 473-487.

Batiha B. Noorani M.S.M. and Hashim I. (2008). Numerical Solutions of the Nonlinear Integro-Differential Equations. International Journal Open Problems Copmt. Math., Vol. 1, No. 1, 34-42

He, Ji-Huan. (2007). Variational Iteration Method-Some recent results and new interpretations. Journal of Computational and Applied Mathematics 207, 3-17.

He, Ji-Huan. (1999). Variational Iteration Method a- kind of non-linear analytical technique: some examples. International J. Non-Linear Mech. 34,699-708.

Hemeda, A. A. (2012). New Iterative Method: Application to nth Order Integro-differential Equations. International Mathematical Forum Vol. 7, 2012, no. 47, 2317 – 2332

Hesamedding E. and Rahimi A. (2013). A New Numerical Scheme for Solving System of Integro-differential Equations Vol, 1, No. 2, 108-199

Lanlege D.I, Momoh S.O and Abuballa A. (2019) Numerical method for solving first order initial value problem in ordinary Differential Equation using picard’s modified euler and runge-kutta method. Journal of Nigerian association of mathematical physics,65-88

Lanlege D.I, Garba U.M and Aluebha A. (2015). Using modified euler method for the solution of some first order differential equations with initial value problems. Pacific Journal of science and technology, No.2,63-88

Lanlege D. I, Garba U.M, Gana U.M and Adetudu M.O. (2015). Application of modified Euler method for the solution of first order differential equation with initial value problem. Journal of Nigerian association of mathematical physics,441-450

Mohyud-din S. T. (2010). Modified Variational Iteration Method for Integro-differential Equations. An International and coupled systems. Verlag der zeitschrift fur Naturforschung, Tubingen, 65a, 277-283

Safavi, M. (2912). The modified Variational Iteration Method for solving Nonlinear Integro-differential Equations. Advances in Information Technology and Management (AITM) Vol. 2, No. 2, 279-282.

Soliman A.A. and Abdou M.A. (2007). Numerical Solutions of nonlinear Evolution Equation using Variational Iteration Method. journal of computational and Applied Mathematics 20.

Sweilam, N. (2007). Fourth order Integro-differential Equations using Integro-differential Equations. An International Iteration Method. An international Journal Computer and Mathematics with Application 54, 1086- 1091.

Tatari M. and Dehghan M. (2007). On the convergence of He’s Variational Iteration method. Journal of Computational and Applied 207, 121-128

Taiwo O. A. Jimoh A. K. (2014). Comparison of some Numerical Methods for The Solution of First and Second Orders Linear Integro-differential Equations. A19merican Journal of Engineering Research (AJER) 03 (01), 245-250.

Wazwaz A. (2011). Linear and Nonlinear Integral Equation method to Nonlinear Integro-differential Equations. Z. Naturforsch . 65a, 418-422.

Yildirim, A. (2010). Application of He’s Variational Iteration method to Nonlinear Integro-differential Equations. Z. Naturforsch. 651, 418- 422

Published

30-04-2023

How to Cite

SOLUTION OF FREDHOLM INTEGRO-DIFFERENTIAL EQUATION BY VARIATIONAL ITERATION METHOD. (2023). FUDMA JOURNAL OF SCIENCES, 7(2), 1-8. https://doi.org/10.33003/fjs-2023-0702-1697

Issue

Vol. 7 No. 2 (2023): FUDMA Journal of Sciences - Vol. 7 No. 2

Section

Research Articles
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FUDMA Journal of Sciences

How to Cite

SOLUTION OF FREDHOLM INTEGRO-DIFFERENTIAL EQUATION BY VARIATIONAL ITERATION METHOD. (2023). FUDMA JOURNAL OF SCIENCES, 7(2), 1-8. https://doi.org/10.33003/fjs-2023-0702-1697