An adaptive algorithm for the Method Approximate Particular Solution (MAPS) using radial basis functions for solving boundary value problems is discussed in this work. The goal of the adaptive algorithm is to construct an optimal collocation points distribution that gives the required accuracy with the smallest number of degrees of freedom. I proposed the formulation of the adaptive MAPS for second order boundary value problems in an arbitrary dimensional setting. Then I applied this method to three different boundary value problems in one-dimensional setting. The performance of the adaptive method has been demonstrated by numerical experiments.
","abstract_html":"<p>An adaptive algorithm for the Method Approximate Particular Solution (MAPS) using radial basis functions for solving boundary value problems is discussed in this work. The goal of the adaptive algorithm is to construct an optimal collocation points distribution that gives the required accuracy with the smallest number of degrees of freedom. I proposed the formulation of the adaptive MAPS for second order boundary value problems in an arbitrary dimensional setting. Then I applied this method to three different boundary value problems in one-dimensional setting. The performance of the adaptive method has been demonstrated by numerical experiments.</p>","abstract_has_math":false,"creators":["Dong, Yichuan"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Masters Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Huiqing Zhu","C.S. Chen","Haiyan Tian"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-05-01T07:00:00Z","date_published":"2014-05-01T07:00:00Z","updated_at":"2026-07-24T05:44:27Z","subjects":["Adaptive Method","MAPS","Boundary Value Problem","Adaptive MAPS"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://aquila.usm.edu/masters_theses/9","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Huiqing Zhu","C.S. Chen","Haiyan Tian"]},{"key":"dc:creator","label":"Author","values":["Dong, Yichuan"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2014-06-20T07:00:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"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":["Adaptive Method","MAPS","Boundary Value Problem","Adaptive MAPS"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://aquila.usm.edu/masters_theses/9"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["An adaptive algorithm for the Method Approximate Particular Solution (MAPS) using radial basis functions for solving boundary value problems is discussed in this work. The goal of the adaptive algorithm is to construct an optimal collocation points distribution that gives the required accuracy with the smallest number of degrees of freedom. I proposed the formulation of the adaptive MAPS for second order boundary value problems in an arbitrary dimensional setting. Then I applied this method to three different boundary value problems in one-dimensional setting. The performance of the adaptive method has been demonstrated by numerical experiments.
"]},{"key":"dc:title","label":"Title","values":["Adaptive Method of Approximate Particular Solution for One-Dimensional Differential Equations"]}]}],"canonical_facts":{"dc:contributor":["Huiqing Zhu","C.S. Chen","Haiyan Tian"],"dc:creator":["Dong, Yichuan"],"dc:date.available":["2014-06-20T07:00:00Z"],"dc:description.abstract":["An adaptive algorithm for the Method Approximate Particular Solution (MAPS) using radial basis functions for solving boundary value problems is discussed in this work. The goal of the adaptive algorithm is to construct an optimal collocation points distribution that gives the required accuracy with the smallest number of degrees of freedom. I proposed the formulation of the adaptive MAPS for second order boundary value problems in an arbitrary dimensional setting. Then I applied this method to three different boundary value problems in one-dimensional setting. The performance of the adaptive method has been demonstrated by numerical experiments.
"],"dc:identifier":["https://aquila.usm.edu/masters_theses/9"],"dc:subject":["Adaptive Method","MAPS","Boundary Value Problem","Adaptive MAPS"],"dc:title":["Adaptive Method of Approximate Particular Solution for One-Dimensional Differential Equations"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Masters Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T05:44:27Z"}