Approximate Solution Of A Class Of Nonlinear Volterra Integral Equations

Abstract

Abstract-In this paper we introduce an approach by an optimization method to find approximate solution for a class of nonlinear Volterra integral equations of the first and second kind. To this purpose, we consider two stages of approximation. First we convert the integral equation to a moment problem and then we modify the new problem to two classes of optimization problems, non-constraint optimization problems and optimal control problems. Finally numerical examples is proposed.

Quasilinearization And Numerical Solution Of Nonlinear Volterra Integro-differential Equations

“…This technique works fruitfully for the problems that their nonlinear parts involve convex or concave functions and gives two sequences of linear problems that their solutions are upper and lower solutions to the nonlinear problem and are converging monotonically and quadratically to the unique solution of the given nonlinear problem. Recently, this method is applied to a variety of problems [2][3][4][5] and in the continuation the convexity assumption was relaxed and the method was generalized and extended in various directions to make it applicable to a large class of problems [6][7][8][9][10][11][12][13][14][15].…”