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.
","abstract_html":"<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>","abstract_has_math":false,"creators":["Acheampong, Kwesi"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Masters Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Huiqing Zhu","Haiyan Tian","C.S. Chen"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-12-01T08:00:00Z","date_published":"2019-12-01T08:00:00Z","updated_at":"2026-07-24T05:45:12Z","subjects":["LocaliMathematics","Approximate","Particular Solutions","Optimal Control Problems","PDES"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://aquila.usm.edu/masters_theses/678","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Huiqing Zhu","Haiyan Tian","C.S. Chen"]},{"key":"dc:creator","label":"Author","values":["Acheampong, Kwesi"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2019-06-21T07:00:00Z"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science (MS)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["LocaliMathematics","Approximate","Particular Solutions","Optimal Control Problems","PDES"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://aquila.usm.edu/masters_theses/678"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["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.
"]},{"key":"dc:title","label":"Title","values":["Localized Method Of Approximate Particular Solutions For Solving Optimal Control Problems Governed By PDES"]}]}],"canonical_facts":{"dc:contributor":["Huiqing Zhu","Haiyan Tian","C.S. Chen"],"dc:creator":["Acheampong, Kwesi"],"dc:date.available":["2019-06-21T07:00:00Z"],"dc:description.abstract":["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.
"],"dc:identifier":["https://aquila.usm.edu/masters_theses/678"],"dc:subject":["LocaliMathematics","Approximate","Particular Solutions","Optimal Control Problems","PDES"],"dc:title":["Localized Method Of Approximate Particular Solutions For Solving Optimal Control Problems Governed By PDES"],"thesis:degree_level":["Masters Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T05:45:12Z"}