Approximation Solution for Initial Value Problem of Singularly Perturbed Integro-Differential Equation

Abstract

Adomian decomposition method (ADM) is used to approximately solve the initial value problem of the singularly perturbed Volterra and Fredholm differential equation. With this method, the desired accurate results are obtained in only a few terms. The approach is simple and effective. An example application is made to demonstrate the effectiveness of ADM. The result obtained is compared with the exact solution. Convergence analysis of the method was performed.

Keywords

• ADM
• Singularly perturbed equation
• Volterra-Fredholm integro-differential equation
• Approximate solution

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