AN OPTIMIZATION METHOD FOR SOLVING THE TWO-DIMENSIONAL NONLINEAR FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND

In this numerical approach, we obtain the solution of the Two-Dimensional Nonlinear Fredholm Integral Equations of the Second Kind problem by converting the problem to an optimal moment problem. The moment problem is modified into one consisting of the minimization of a positive linear functional over a set of Radon measures. Then we obtain an optimal measure which is approximated by a finite combination of atomic measures and by using atomic measures we change this one to a semi-infinite dimensional linear programming problem. We approximate the latter one by a finite dimensional linear programming problem.

کلیدواژه ها:

Optimization ، nonlinear Fredholm integral equation ، optimal moment problem ، measure