Homotopy Analysis Method For Nonlinear Ordinary Eigenvalue Problems

<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>

Name thesis:degree_name

Master of Science (MS)

Level thesis:degree_level

Masters Thesis

Year dc:date.available

2020

Author dc:creator

• Perera, Subagya

Contributors dc:contributor

• Dr. Haiyan Tian
• Dr. James Lambers
• Dr. Huiqing Zhu

• 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

Repository record dc:identifier

https://aquila.usm.edu/masters_theses/720

OAI identifier oai:identifier

oai:aquila.usm.edu:masters_theses-1789