Solving nonlinear Fredholm integro-differential equations via modifications of some numerical methods

Authors : Fawziah ALSAAR, Kirtiwant GHADLE

Pages : 260-276

Doi:10.31197/atnaa.872432

View : 53 | Download : 6

Publication Date : 2021-06-30

Article Type : Research Paper

Abstract :The paper presents the modifications of the variational iteration method insert ignore into journalissuearticles values(MVIM);, Laplace Adomian decomposition method insert ignore into journalissuearticles values(MLADM);, and the homotopy perturbation method insert ignore into journalissuearticles values(MHPM); for solving the nonlinear Fredholm integro-differential equation of the second kind. In these methods a series is created, the summation of which gives the solution of the discussed equation. Conditions ensuring convergence of this series are presented in the paper. An example illustrating the usage of the investigated methods is presented as well and the results reveal that the proposed methods are very effective, able, and simple. comparison between our proposed methods with the exact solution and some traditional methods is presented during a numerical example. The results reveal that insert ignore into journalissuearticles values(MHPM); and insert ignore into journalissuearticles values(MLADM); lead to an exact solution and insert ignore into journalissuearticles values(MVIM); leads to a limited solution. The uniqueness of the solutions and the convergence of the proposed methods are also proved.
Keywords : Nonlinear Fredholm integro differential equation, modification of the variational iteration method MVIM, modification of homotopy perturbation method MHPM, modif

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