The modified decomposition method for solving Volterra integral equation of the second kind using Maple

Abstract

In this paper, Volterra Integral equations of the second kind arise in several applications. These include applications in biology, physics, chemistry and engineering. In recent years, much work has been carried out by researchers in mathematics and engineering in applying and analyzing novel numerical and semi-analytical methods for obtaining solutions of integral equations of the second kind. The Modified Decomposition Method for solving Volterra integral equations of the second kind by using Maple program, By the Taylor expansion of components apart from the zeroth term of the Adomian series solution. Some numerical examples are provided to demonstrate the validity of the method, so all calculations can be easily using Maple to find that exact solution. In the current paper, the principle of the Modified decomposition method is described and its advantages are Some illustrative examples are presented and the results show that the solutions obtained by using this technique have a close agreement with series solutions obtained with the help of the Modified Decomposition Method using Maple17.