Localized Method Of Approximate Particular Solutions For Solving Optimal Control Problems Governed By PDES

In this thesis, the method of approximate particular solutions(MAPS) and localized method of approximate particular solutions(LMAPS) with polynomial basis, and radial basis functions are proposed and applied on the optimal control problems(OCPs) governed by partial differential equations(PDEs). This study proceeds in several steps. First, polynomial basis and radial basis functions are used to globally approximate solutions for the PDEs which have been combined into a single matrix system numerically from the optimality conditions of the OCPs. Secondly, polynomial and radial basis functions are used to locally approximate particular solutions for the same matrix system numerically. We use these approaches to two types of problems, a smooth and singular problem. The first example numerically experiments on a square domain and the second example on an L-shaped disc domain. These approaches are tested and compared. The results show our proposed method for solving optimal control problems governed by partial differential equations works

Informed Consent under the Ghana Health Service Patients Charter: Practice and Awareness

6

Improved Geometric Modeling Using the Method of Fundamental Solutions

In this paper, we propose a new geometric model that includes a fourth-order partial differential equation (PDE) for reconstructing 2D curves. For instance, we use this model to reproduce letters in Time Roman font. The method of fundamental solutions (MFS), which is a simple and easily implemented meshless method, is employed for solving the proposed PDEs. In addition, no fictitious boundary is required for the proposed MFS formulation, which further simplifies the implementation of the numerical method. Three examples of 2D curve reproduction are presented to demonstrate the effectiveness of the proposed model