A novel meshless method to solve a class of PDE constrainted optimization problems

In this paper, we discuss the application of a hybrid local meshless method to solve PDE constrainted optimization problem. The presented local meshless method is based on the linear combination of moving least squares (MLS) and local radial basis functions (LRBF) in the same compact support, this method will change between interpolation and approximation. The aim of this paper is to solve the system of cupled partial differential equation of necessary and sufficient conditions for distributed optimal control problem by combination of MLS and LRBF. To keep matters simple, the problem has been considered in one-dimensional case, however the techniques can be employed for two- and three-dimensionals cases. Several test problems are employed and results of numerical experiments are presented. The obtained results confirm the acceptable accuracy of the proposed methods.