Date of Award
Spring 2020
Degree Type
Masters Thesis
Degree Name
Master of Science (MS)
School
Mathematics and Natural Sciences
Committee Chair
Dr. Haiyan Tian
Committee Chair School
Mathematics and Natural Sciences
Committee Member 2
Dr. James Lambers
Committee Member 2 School
Mathematics and Natural Sciences
Committee Member 3
Dr. Huiqing Zhu
Committee Member 3 School
Mathematics and Natural Sciences
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.
ORCID ID
https://orcid.org/0000-0002-5616-1415
Copyright
2020, Subagya Perera
Recommended Citation
Perera, Subagya, "Homotopy Analysis Method For Nonlinear Ordinary Eigenvalue Problems" (2020). Master's Theses. 720.
https://aquila.usm.edu/masters_theses/720
Included in
Ordinary Differential Equations and Applied Dynamics Commons, Other Applied Mathematics Commons, Other Mathematics Commons