Numerical solving Volterra integral equations by linear programming

In this paper, a new approach is introduced to find approximate solutions of linear Volterra integral equations (of both kinds) using the minimization of residual functions based on the infinity norm. Since, this minimization problem is not simple to solve numerically, an efficient algorithm is presented for finding a numerical solution based on linear programming. Also, the existence and the convergence of approximate solutions based on this approach are investigated. In order to confirm the efficiency and accuracy of the proposed method, some numerical examples are examined.