In the past, dealing with fourth-order partial differential equations using the Local Method was not reliable due to difficulties in solving them directly. An approach such as splitting these equations into two Poisson differential equations was adopted to alleviate such challenges. However, this has a limitation since it is only applicable to Dirichlet and Laplace boundary conditions. In this paper, we solve fourth-order PDEs directly using the LMAPS. The improvement on the accuracy of this method was as a result of the proposed distribution of boundary conditions to alternating boundary points. And, also the use of suitable shape parameter; calculated using LOOCV(Leave-One-Out-Cross-Validation) Algorithm. The effectiveness of this Method was evident when we compared the results from two numerical examples.
","abstract_html":"<p>In the past, dealing with fourth-order partial differential equations using the Local Method was not reliable due to difficulties in solving them directly. An approach such as splitting these equations into two Poisson differential equations was adopted to alleviate such challenges. However, this has a limitation since it is only applicable to Dirichlet and Laplace boundary conditions. In this paper, we solve fourth-order PDEs directly using the LMAPS. The improvement on the accuracy of this method was as a result of the proposed distribution of boundary conditions to alternating boundary points. And, also the use of suitable shape parameter; calculated using LOOCV(Leave-One-Out-Cross-Validation) Algorithm. The effectiveness of this Method was evident when we compared the results from two numerical examples.</p>","abstract_has_math":false,"creators":["Amuzu, Lionel"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Masters Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":["C.S. Chen","James Lambers","Huiqing Zhu"],"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":["Localized","method","of","approximate","particular","solution"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://aquila.usm.edu/masters_theses/683","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["C.S. Chen","James Lambers","Huiqing Zhu"]},{"key":"dc:creator","label":"Author","values":["Amuzu, Lionel"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2019-10-18T07:00:00Z"]},{"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":["Localized","method","of","approximate","particular","solution"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://aquila.usm.edu/masters_theses/683"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In the past, dealing with fourth-order partial differential equations using the Local Method was not reliable due to difficulties in solving them directly. An approach such as splitting these equations into two Poisson differential equations was adopted to alleviate such challenges. However, this has a limitation since it is only applicable to Dirichlet and Laplace boundary conditions. In this paper, we solve fourth-order PDEs directly using the LMAPS. The improvement on the accuracy of this method was as a result of the proposed distribution of boundary conditions to alternating boundary points. And, also the use of suitable shape parameter; calculated using LOOCV(Leave-One-Out-Cross-Validation) Algorithm. The effectiveness of this Method was evident when we compared the results from two numerical examples.
"]},{"key":"dc:title","label":"Title","values":["Localized Method of Approximate Particular Solutions for Solving Fourth-Order PDEs"]}]}],"canonical_facts":{"dc:contributor":["C.S. Chen","James Lambers","Huiqing Zhu"],"dc:creator":["Amuzu, Lionel"],"dc:date.available":["2019-10-18T07:00:00Z"],"dc:description.abstract":["In the past, dealing with fourth-order partial differential equations using the Local Method was not reliable due to difficulties in solving them directly. An approach such as splitting these equations into two Poisson differential equations was adopted to alleviate such challenges. However, this has a limitation since it is only applicable to Dirichlet and Laplace boundary conditions. In this paper, we solve fourth-order PDEs directly using the LMAPS. The improvement on the accuracy of this method was as a result of the proposed distribution of boundary conditions to alternating boundary points. And, also the use of suitable shape parameter; calculated using LOOCV(Leave-One-Out-Cross-Validation) Algorithm. The effectiveness of this Method was evident when we compared the results from two numerical examples.
"],"dc:identifier":["https://aquila.usm.edu/masters_theses/683"],"dc:subject":["Localized","method","of","approximate","particular","solution"],"dc:title":["Localized Method of Approximate Particular Solutions for Solving Fourth-Order PDEs"],"thesis:degree_level":["Masters Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T05:45:12Z"}