Numerical solving initial value problem for Fredholm type linear integro-differential equation system

In this paper, we introduce a numerical method for solving initial value problems for a system of linear integro-differential equations. The main idea is based on the interpolations of unknown functions at distinct interpolation points. We next use Clenshaw-Curtis quadrature formulae required in the approximation of the integral equations. The technique is very effective and simple. In the end, to show the efficiency of this method, we present some numerical examples.