We consider a time-dependent method which is coupled with the method of approximate particular solutions (MAPS) of Delta-shaped basis functions and the method of fundamental solutions (MFS) to solve nonlinear ordinary differential equations. Firstly, we convert a nonlinear problem into a sequence of time-dependent non-homogeneous boundary value problems through a fictitious time integration method. The superposition principle is applied to split the numerical solution at each time step into an approximate particular solution and a homogeneous solution. Delta-shaped basis functions are used to provide an approximation of the source function at each time step. The purpose of this is to allow a convenient derivation of an approximate particular solution. The corresponding homogeneous boundary value problem is solved using the method of fundamental solutions. Numerical results support the accuracy and validity of this computational method.
","abstract_html":"<p>We consider a time-dependent method which is coupled with the method of approximate particular solutions (MAPS) of Delta-shaped basis functions and the method of fundamental solutions (MFS) to solve nonlinear ordinary differential equations. Firstly, we convert a nonlinear problem into a sequence of time-dependent non-homogeneous boundary value problems through a fictitious time integration method. The superposition principle is applied to split the numerical solution at each time step into an approximate particular solution and a homogeneous solution. Delta-shaped basis functions are used to provide an approximation of the source function at each time step. The purpose of this is to allow a convenient derivation of an approximate particular solution. The corresponding homogeneous boundary value problem is solved using the method of fundamental solutions. Numerical results support the accuracy and validity of this computational method.</p>","abstract_has_math":false,"creators":["Ocloo, Cyril"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Masters Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Haiyan Tian","James Lambers","Huiqing Zhu"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-05-01T07:00:00Z","date_published":"2020-05-01T07:00:00Z","updated_at":"2026-07-24T05:45:19Z","subjects":["Time","integration","method","Numerical Analysis and Computation","Ordinary Differential Equations and Applied Dynamics","Other Applied Mathematics","Partial Differential Equations"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://aquila.usm.edu/masters_theses/729","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Haiyan Tian","James Lambers","Huiqing Zhu"]},{"key":"dc:creator","label":"Author","values":["Ocloo, Cyril"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.available","label":"Dc Date Available","values":["2026-05-14T07:00:00Z"]},{"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":["Time","integration","method","Numerical Analysis and Computation","Ordinary Differential Equations and Applied Dynamics","Other Applied Mathematics","Partial Differential Equations"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://aquila.usm.edu/masters_theses/729"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We consider a time-dependent method which is coupled with the method of approximate particular solutions (MAPS) of Delta-shaped basis functions and the method of fundamental solutions (MFS) to solve nonlinear ordinary differential equations. Firstly, we convert a nonlinear problem into a sequence of time-dependent non-homogeneous boundary value problems through a fictitious time integration method. The superposition principle is applied to split the numerical solution at each time step into an approximate particular solution and a homogeneous solution. Delta-shaped basis functions are used to provide an approximation of the source function at each time step. The purpose of this is to allow a convenient derivation of an approximate particular solution. The corresponding homogeneous boundary value problem is solved using the method of fundamental solutions. Numerical results support the accuracy and validity of this computational method.
"]},{"key":"dc:title","label":"Title","values":["A Time Integration Method of Approximate Particular Solutions for Nonlinear Ordinary Differential Equations"]}]}],"canonical_facts":{"dc:contributor":["Haiyan Tian","James Lambers","Huiqing Zhu"],"dc:creator":["Ocloo, Cyril"],"dc:date.available":["2026-05-14T07:00:00Z"],"dc:description.abstract":["We consider a time-dependent method which is coupled with the method of approximate particular solutions (MAPS) of Delta-shaped basis functions and the method of fundamental solutions (MFS) to solve nonlinear ordinary differential equations. Firstly, we convert a nonlinear problem into a sequence of time-dependent non-homogeneous boundary value problems through a fictitious time integration method. The superposition principle is applied to split the numerical solution at each time step into an approximate particular solution and a homogeneous solution. Delta-shaped basis functions are used to provide an approximation of the source function at each time step. The purpose of this is to allow a convenient derivation of an approximate particular solution. The corresponding homogeneous boundary value problem is solved using the method of fundamental solutions. Numerical results support the accuracy and validity of this computational method.
"],"dc:identifier":["https://aquila.usm.edu/masters_theses/729"],"dc:subject":["Time","integration","method","Numerical Analysis and Computation","Ordinary Differential Equations and Applied Dynamics","Other Applied Mathematics","Partial Differential Equations"],"dc:title":["A Time Integration Method of Approximate Particular Solutions for Nonlinear Ordinary Differential Equations"],"thesis:degree_level":["Masters Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T05:45:19Z"}