A different approach for solving the nonlinear Fredholm integral equations of the second kind

摘要

In this paper, we proposed a method for finding a approximate solution for the nonlinear Fredholm integral equations of the second kind. In this approach, the nonlinearity of the kernel has no serious effect on the convergence of the solution. First, we convert the problem to an optimal control problem by introducing an artificial control function. Then by using some concepts of measure theory, we make a metamorphosis in the space of the problem and finally we will get a linear programming whose solution gives rise to the approximate solution of the integral equation.