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

<p>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).</p> <p>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.</p>

Name thesis:degree_name

Master of Science (MS)

Level thesis:degree_level

Masters Thesis

Year dc:date.available

2019

Author dc:creator

• Acheampong, Kwesi

Contributors dc:contributor

• Huiqing Zhu
• Haiyan Tian
• C.S. Chen

• LocaliMathematics
• Approximate
• Particular Solutions
• Optimal Control Problems
• PDES

Repository record dc:identifier

https://aquila.usm.edu/masters_theses/678

OAI identifier oai:identifier

oai:aquila.usm.edu:masters_theses-1725