NUMERICAL SOLUTION OF LINEAR FREDHOLM AND VOLTERRA INTEGRAL EQUATIONS USING OPTIMAL CONTROL TECHNIQUES COMBINED WITH REGULARIZATION METHOD

This paper describes a new method to obtain the numerical solution of linear Fredholm and Volterra integral equations of the first and second kind by means of an optimal control technique. First, integral equations are transformed to a parametric optimization problem subject to algebric constraints. Then control and state variables will be approximated by chebychev series. To deal with ill-posed first kind Fredholm and Volterra integral equations the regularization method combined with the optimal control technique is applied. Numerical results are very promising.