The purpose of this thesis is to solve biharmonic boundary value problems using two different boundary methods and compare their performances. The two boundary methods used are the method of fundamental solutions (MFS) and the method of approximate fundamental solutions (MAFS). The Delta-shaped basis function with the Abel regularization technique is used in the construction of the approximate fundamental solutions in MAFS. The MFS produces more accurate results but needs known fundamental solutions for the differential operator. The MAFS can provide comparable results, and is applicable to more general differential operators. The numerical results using both methods are presented.
","abstract_html":"<p>The purpose of this thesis is to solve biharmonic boundary value problems using two different boundary methods and compare their performances. The two boundary methods used are the method of fundamental solutions (MFS) and the method of approximate fundamental solutions (MAFS). The Delta-shaped basis function with the Abel regularization technique is used in the construction of the approximate fundamental solutions in MAFS. The MFS produces more accurate results but needs known fundamental solutions for the differential operator. The MAFS can provide comparable results, and is applicable to more general differential operators. The numerical results using both methods are presented.</p>","abstract_has_math":false,"creators":["Oh, Jaeyoun"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Masters Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Haiyan Tian","Joseph Kolibal","James Lambers"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012-05-01T07:00:00Z","date_published":"2012-05-01T07:00:00Z","updated_at":"2026-07-24T05:45:06Z","subjects":["Mathematics","Physical Sciences and Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://aquila.usm.edu/masters_theses/508","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Haiyan Tian","Joseph Kolibal","James Lambers"]},{"key":"dc:creator","label":"Author","values":["Oh, Jaeyoun"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2018-11-15T08:00:00Z"]},{"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":["Mathematics","Physical Sciences and Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://aquila.usm.edu/masters_theses/508"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The purpose of this thesis is to solve biharmonic boundary value problems using two different boundary methods and compare their performances. The two boundary methods used are the method of fundamental solutions (MFS) and the method of approximate fundamental solutions (MAFS). The Delta-shaped basis function with the Abel regularization technique is used in the construction of the approximate fundamental solutions in MAFS. The MFS produces more accurate results but needs known fundamental solutions for the differential operator. The MAFS can provide comparable results, and is applicable to more general differential operators. The numerical results using both methods are presented.
"]},{"key":"dc:title","label":"Title","values":["A Comparison of Two Boundary Methods For Biharmonic Boundary Value Problems"]}]}],"canonical_facts":{"dc:contributor":["Haiyan Tian","Joseph Kolibal","James Lambers"],"dc:creator":["Oh, Jaeyoun"],"dc:date.available":["2018-11-15T08:00:00Z"],"dc:description.abstract":["The purpose of this thesis is to solve biharmonic boundary value problems using two different boundary methods and compare their performances. The two boundary methods used are the method of fundamental solutions (MFS) and the method of approximate fundamental solutions (MAFS). The Delta-shaped basis function with the Abel regularization technique is used in the construction of the approximate fundamental solutions in MAFS. The MFS produces more accurate results but needs known fundamental solutions for the differential operator. The MAFS can provide comparable results, and is applicable to more general differential operators. The numerical results using both methods are presented.
"],"dc:identifier":["https://aquila.usm.edu/masters_theses/508"],"dc:subject":["Mathematics","Physical Sciences and Mathematics"],"dc:title":["A Comparison of Two Boundary Methods For Biharmonic Boundary Value Problems"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Masters Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T05:45:06Z"}