Abstract
The main aim of this paper is to apply a new technique suggested by Temimi and Ansari namely (TAM) for solving higher order Integro-Differential Equations. These equations are commonly hard to handle analytically so it is request numerical methods to get an efficient approximate solution. Series solutions of the problem under consideration are presented by means of the Iterative Method (IM). The numerical results show that the method is effective, accurate and easy to implement rapidly convergent series to the exact solution with minimum amount of computation. The MATLAB is used as a software for the calculations.
Highlights
Integro-Differential Equations (IDEs) include in many mathematical formulations of physical phenomena, these problems have a major role of interest and arise in many applications in various fields of science, such as chemical kinetics, fluid dynamics, engineering problems and biological models
Several numerical examples are introduced and comparison with existing methods, the results reveal that the method is accurate and easy to implement
The obtained solutions can be shown as a series form that converges to the exact solution with simple computations
Summary
Integro-Differential Equations (IDEs) include in many mathematical formulations of physical phenomena, these problems have a major role of interest and arise in many applications in various fields of science, such as chemical kinetics, fluid dynamics, engineering problems and biological models. Temimi and Ansari (TAM) have been suggested a new iterative method, i.e., Semi Analytic Iterative Method (SAIM) for solving linear and nonlinear functional equations [14] This method has been extensively studied by many researchers recently; it has been successfully applied for solving some linear and nonlinear partial and ordinary differential equations [15,16,17,18]. It is worth mentioning, SAIM is not yet used to solve higher order IDEs. It is worth mentioning, SAIM is not yet used to solve higher order IDEs This method is accurate and powerful technique, needn’t to impose any additional restrictions to get the numerical solution of these problems.
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