Abstract
In this article, we introduce a modification of the Taylor matrix method using Pade approximation to obtain an accurate solution of linear system of Fredholm integro-differential equations (FIDEs). This modification is based on, first, taking truncated Taylor series of the functions and then substituting their matrix forms into the given equations. Thereby the equation reduces to a matrix equation, which corresponds to a system of linear algebraic equations with unknown Taylor coefficients. Finally, we use Pade approximation to obtain an accurate numerical solution of the proposed problem. To demonstrate the validity and the applicability of the proposed method, we present some numerical examples. A comparison with the standard Taylor matrix method is given.