Solving of second order nonlinear PDE problems by using artificial controls with controlled error

Abstract

In this paper, we find the approximate solution of a second order nonlinear partial differential equation on a simple connected region in R2. We transfer this problem to a new problem of second order non-linear partial differential equation on a rectangle. Then, we transformed the later one to an equivalent optimization problem. Then we consider the optimization problem as a distributed parameter system with artificial controls. Finally, by using the theory of measure, we obtain the approximate solution of the original problem. In this paper also the global error in L1 is controlled.