Abstract
In this paper, Vito Volterra studied the phenomenon of population growth, and new types of equations have been developed and termed as the integro-differential equation. Here we will address the Mixed Volterra Fredholm integro-differential equation. We introduce some basic idea of Modified Decomposition method (MDM) to solve the Volterra-Fredholm integro-differential equation. The modified decomposition method (MDM) is applied to solve the Volterra Fredholm integro-differential equation. Based on the proposed after treatment technique, the truncated series solution obtained by the Modified Decomposition method (MDM) can be expressed as another series in terms of the independent sine and cosine trigonometric functions. In addition, examples that illustrate the pertinent features of this method is presented, and results of the study is discussed. Also, we compare the result with exact solution, and we investigate the error between numerical solution and exact solution and draw the graph of function by using Maple18. Finally, the results reveal that the Modified Decomposition method is very effective and convenient for solving Volterra Fredholm integro-differential equation.