Abstract
In this paper, linear and non-linear Fredholm Integro-Differential Equations with initial conditions are presented. Aiming to find out an analytic and approximate solutions to linear and non-linear Fredholm Integro-Differential Equations, this paper presents a comparative study of He’s Homotopy perturbation method with other traditional methods namely the Variational iteration method (VIM), the Adomian decomposition method (ADM), the Series solution method (SSM) and the Direct computation method (DCM). Comparison of the applied methods of analytic solutions reveals that He’s Homotopy perturbation method is tremendously powerful and effective mathematical tool.
Highlights
Many researchers and scientists studied the integrodifferential equations through their work in science applications like heat transformer, neutron diffusion, and biological species coexisting together with increasing and decreasing rates of generating and diffusion process in general
Variational iteration method, Adomian decomposition method, series solution method, and Direct computation method have been applied to analyze the behavior of the solution of fredholm integrodifferential equations
This paper shows He’s Homotopy perturbation method of solving linear and non-linear Fredholm Integro-Differential Equation and conducted a comparative study between He’s Homotopy perturbation method and the traditional methods that is Variational iteration method, Adomian decomposition method, Series solution method and Direct computation method
Summary
Many researchers and scientists studied the integrodifferential equations through their work in science applications like heat transformer, neutron diffusion, and biological species coexisting together with increasing and decreasing rates of generating and diffusion process in general These kinds of equations can be found in physics, biology and engineering applications, as well as in models dealing with advanced integral equations such as [12], [22,23]. This paper shows a comparative study between He's Homotopy perturbation method [8,9,10,11,12,13,14,15,16,17,18,19] and four traditional methods for analytic treatments of linear and nonlinear integro-differential equations. For p=1, the approximate solution of equation (1) can be expressed as
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