We use the methods of compactly supported radial basis functions (CS-RBFs) and Delta-shaped basis functions (DBFs) to obtain the numerical solution of a two-dimensional biharmonic boundary value problem. The biharmonic equation is difficult to solve due to its existing fourth order derivatives, besides it requires more than one boundary conditions on the same part of the boundary. In this thesis, we use either a one-level or a two-level technique for constructing the approximate solution in the context of Kansa’s collocation method. This thesis will compare the accuracy of the methods of CS-RBFs and DBFs when applied to the biharmonic boundary value problem. Both methods can be used on an irregular shaped domain. Numerical results show that the DBF approach is superior than that of the CS-RBF.
","abstract_html":"<p>We use the methods of compactly supported radial basis functions (CS-RBFs) and Delta-shaped basis functions (DBFs) to obtain the numerical solution of a two-dimensional biharmonic boundary value problem. The biharmonic equation is difficult to solve due to its existing fourth order derivatives, besides it requires more than one boundary conditions on the same part of the boundary. In this thesis, we use either a one-level or a two-level technique for constructing the approximate solution in the context of Kansa’s collocation method. This thesis will compare the accuracy of the methods of CS-RBFs and DBFs when applied to the biharmonic boundary value problem. Both methods can be used on an irregular shaped domain. Numerical results show that the DBF approach is superior than that of the CS-RBF.</p>","abstract_has_math":false,"creators":["Richardson, Megan LaShea"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Masters Thesis","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Haiyan Tan","Joseph Kolibal","C.S. Chen"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-08-01T07:00:00Z","date_published":"2011-08-01T07:00:00Z","updated_at":"2026-07-24T05:44:41Z","subjects":["biharmonic boundary valve problems","Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://aquila.usm.edu/masters_theses/213","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Haiyan Tan","Joseph Kolibal","C.S. Chen"]},{"key":"dc:creator","label":"Author","values":["Richardson, Megan LaShea"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2016-08-12T07:00:00Z"]},{"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":["biharmonic boundary valve problems","Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://aquila.usm.edu/masters_theses/213"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We use the methods of compactly supported radial basis functions (CS-RBFs) and Delta-shaped basis functions (DBFs) to obtain the numerical solution of a two-dimensional biharmonic boundary value problem. The biharmonic equation is difficult to solve due to its existing fourth order derivatives, besides it requires more than one boundary conditions on the same part of the boundary. In this thesis, we use either a one-level or a two-level technique for constructing the approximate solution in the context of Kansa’s collocation method. This thesis will compare the accuracy of the methods of CS-RBFs and DBFs when applied to the biharmonic boundary value problem. Both methods can be used on an irregular shaped domain. Numerical results show that the DBF approach is superior than that of the CS-RBF.
"]},{"key":"dc:title","label":"Title","values":["A Comparison of Two Different Methods for Solving Biharmonic Boundary Valve Problems"]}]}],"canonical_facts":{"dc:contributor":["Haiyan Tan","Joseph Kolibal","C.S. Chen"],"dc:creator":["Richardson, Megan LaShea"],"dc:date.available":["2016-08-12T07:00:00Z"],"dc:description.abstract":["We use the methods of compactly supported radial basis functions (CS-RBFs) and Delta-shaped basis functions (DBFs) to obtain the numerical solution of a two-dimensional biharmonic boundary value problem. The biharmonic equation is difficult to solve due to its existing fourth order derivatives, besides it requires more than one boundary conditions on the same part of the boundary. In this thesis, we use either a one-level or a two-level technique for constructing the approximate solution in the context of Kansa’s collocation method. This thesis will compare the accuracy of the methods of CS-RBFs and DBFs when applied to the biharmonic boundary value problem. Both methods can be used on an irregular shaped domain. Numerical results show that the DBF approach is superior than that of the CS-RBF.
"],"dc:identifier":["https://aquila.usm.edu/masters_theses/213"],"dc:subject":["biharmonic boundary valve problems","Mathematics"],"dc:title":["A Comparison of Two Different Methods for Solving Biharmonic Boundary Valve Problems"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Masters Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T05:44:41Z"}