Zahra Shabani - Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan, I.R.Iran
Haleh Tajadodi - Department of Mathematics, Faculty of Mathematics, University of Sistan and Baluchestan, Zahedan Iran.

In this paper, a numerical technique is proposed to solve optimal control problems (OPCs) of Volterra integral equations (VIEs). We apply the linear B-spline polynomials to solve OPCs by VIEs. The B-spline function divides the interval into sub-intervals and then built a different approximating polynomial on each sub-interval. In this method, optimal trajectory and control functions are expanded in terms of B-spline functions. The linear B-spline operational matrix of integration and multiplication are utilized in the proposed method.The main characteristic this method is that by using the suggested numerical technique and the related operational matrices, optimal control problem governed by Volterra integral equations is converted to a system of equations. Suffice it to say that this scheme simplifies The main problems and also makes to obtain a good approximate solution for them. In the end, there are two illustrative examples which numerical results show the validity and applicability of our method.

Optimal control problems, Volterra integral equations, Linear B-spline function, Operational matrix