In this thesis, we solve nonlinear differential equations by the homotopy analysis method (HAM), which is a semi-analytic method first introduced by Shijun Liao in 1992. The modified HAM can be viewed as a more generalized method that encloses many perturbation and non-perturbation methods. It is different from perturbation or other analytical methods in that it allows considerable freedomformanyvariables. Using the modified HAM, especially zero-order and higher-order deformation equations, we solve a nonlinear initial value problem and a nonlinear eigenvalue problem. We adjust the convergence region of a solution by modifying auxiliary parameter values. The results converge in very few iterations under the proper choice of the values of auxiliary parameters. The approach is shown to be accurate and valid for differential equations with strong nonlinearity.
Keywords: Nonlinear initial value problem, Nonlineareigenvalueproblem, Homotopy analysis method, Duffing's equation, Perturbation theory.
","abstract_html":"<p>In this thesis, we solve nonlinear differential equations by the homotopy analysis method (HAM), which is a semi-analytic method first introduced by Shijun Liao in 1992. The modified HAM can be viewed as a more generalized method that encloses many perturbation and non-perturbation methods. It is different from perturbation or other analytical methods in that it allows considerable freedomformanyvariables. Using the modified HAM, especially zero-order and higher-order deformation equations, we solve a nonlinear initial value problem and a nonlinear eigenvalue problem. We adjust the convergence region of a solution by modifying auxiliary parameter values. The results converge in very few iterations under the proper choice of the values of auxiliary parameters. The approach is shown to be accurate and valid for differential equations with strong nonlinearity.</p> <p>Keywords: Nonlinear initial value problem, Nonlineareigenvalueproblem, Homotopy analysis method, Duffing's equation, Perturbation theory.</p>","abstract_has_math":false,"creators":["Perera, Subagya"],"institution":null,"degree_name":"Master of Science (MS)","degree_level":"Masters Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Dr. Haiyan Tian","Dr. James Lambers","Dr. 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":["Nonlinear initial value problem","Nonlinear eigenvalue problem","Homotopy analysis method","Duffing's equation","Perturbation theory","Differential Equation.","Ordinary Differential Equations and Applied Dynamics","Other Applied Mathematics","Other Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://aquila.usm.edu/masters_theses/720","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dr. Haiyan Tian","Dr. James Lambers","Dr. Huiqing Zhu"]},{"key":"dc:creator","label":"Author","values":["Perera, Subagya"]}]},{"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":["Nonlinear initial value problem","Nonlinear eigenvalue problem","Homotopy analysis method","Duffing's equation","Perturbation theory","Differential Equation.","Ordinary Differential Equations and Applied Dynamics","Other Applied Mathematics","Other Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://aquila.usm.edu/masters_theses/720"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, we solve nonlinear differential equations by the homotopy analysis method (HAM), which is a semi-analytic method first introduced by Shijun Liao in 1992. The modified HAM can be viewed as a more generalized method that encloses many perturbation and non-perturbation methods. It is different from perturbation or other analytical methods in that it allows considerable freedomformanyvariables. Using the modified HAM, especially zero-order and higher-order deformation equations, we solve a nonlinear initial value problem and a nonlinear eigenvalue problem. We adjust the convergence region of a solution by modifying auxiliary parameter values. The results converge in very few iterations under the proper choice of the values of auxiliary parameters. The approach is shown to be accurate and valid for differential equations with strong nonlinearity.
Keywords: Nonlinear initial value problem, Nonlineareigenvalueproblem, Homotopy analysis method, Duffing's equation, Perturbation theory.
"]},{"key":"dc:title","label":"Title","values":["Homotopy Analysis Method For Nonlinear Ordinary Eigenvalue Problems"]}]}],"canonical_facts":{"dc:contributor":["Dr. Haiyan Tian","Dr. James Lambers","Dr. Huiqing Zhu"],"dc:creator":["Perera, Subagya"],"dc:date.available":["2026-05-14T07:00:00Z"],"dc:description.abstract":["In this thesis, we solve nonlinear differential equations by the homotopy analysis method (HAM), which is a semi-analytic method first introduced by Shijun Liao in 1992. The modified HAM can be viewed as a more generalized method that encloses many perturbation and non-perturbation methods. It is different from perturbation or other analytical methods in that it allows considerable freedomformanyvariables. Using the modified HAM, especially zero-order and higher-order deformation equations, we solve a nonlinear initial value problem and a nonlinear eigenvalue problem. We adjust the convergence region of a solution by modifying auxiliary parameter values. The results converge in very few iterations under the proper choice of the values of auxiliary parameters. The approach is shown to be accurate and valid for differential equations with strong nonlinearity.
Keywords: Nonlinear initial value problem, Nonlineareigenvalueproblem, Homotopy analysis method, Duffing's equation, Perturbation theory.
"],"dc:identifier":["https://aquila.usm.edu/masters_theses/720"],"dc:subject":["Nonlinear initial value problem","Nonlinear eigenvalue problem","Homotopy analysis method","Duffing's equation","Perturbation theory","Differential Equation.","Ordinary Differential Equations and Applied Dynamics","Other Applied Mathematics","Other Mathematics"],"dc:title":["Homotopy Analysis Method For Nonlinear Ordinary Eigenvalue Problems"],"thesis:degree_level":["Masters Thesis"],"thesis:degree_name":["Master of Science (MS)"]},"updated_at":"2026-07-24T05:45:19Z"}