Abstract-In this paper we present a new approach for linear Volterra integral equations that is based on optimal control theory. S ome optimal control problems corresponding Volterra integral equation be introduced which we solve these problems by discretization methods and linear programming approaches. Finally, some examples are given to show the efficiency of approach.Index Terms -Volterra integral equations, Optimal control, Linear programming.
I. INTRO DUCTIO NVo lterra integral equations arise in many physical applications, e.g., potential theory and Dirichlet problems and electrostatics. Also, Volterra integral equations are applied in the biology, chemistry, engineering, mathematical problems of radiat ion equilibriu m, the particle transport problems of astrophysics and reactor theory, and radiation heat transfer problems [1,2,3,4,5]. There exist the some valid appro ximate and numerical methods for solving Vo lterra integral equation such as Adomian decomposition method [6], Walsh functions method and mult igrid approach [7,8] [35,36,37,38,39]. In this paper, we present a d ifferent approach fro m above methods for solving linear volterra integral equations which is based on the optimal control theory [40,41,42]. Consider the following linear Vo lterra integral equations of second kind: ( ) ( ) ( , ) ( ) , [ , ],