An Algorithm for Solving Linear and Non-Linear Volterra Integro-Differential Equations.

Using Mathematica computer software, a numerical procedure called the modified Adomian decomposition method (MADM) is successfully implemented for obtaining exact solutions of some classes of Volterra integro-differential equations based on the ADM approximate series solutions, Laplace transform, and Pade approximants. The reliability and effectiveness of MADM are tested in some examples. The obtained results indicate that the implemented procedure is very effective and powerful for handling this kind of differential equation and is valid for a wide class of other types of differential equations. [ABSTRACT FROM AUTHOR]