Numerical solutions of system of linear Fredholm–Volterra integro-differential equations by the Bessel collocation method and error estimation

In this study, the Bessel collocation method is presented for the solutions of system of linear Fredholm–Volterra integro-differential equations which includes the derivatives of unknown functions in integral parts. The Bessel collocation method transforms the problem into a system of linear algebraic equations by means of the Bessel functions of first kind, the collocation points and the matrix relations. Also, an error estimation is given for the considered problem and the method. Illustrative examples are presented to show efficiency of method and the comparisons are made with the results of other methods. All of numerical calculations have been made on a computer using a program written in Matlab.