Date of Award
Spring 2020
Degree Type
Masters Thesis
Degree Name
Master of Science (MS)
School
Mathematics and Natural Sciences
Committee Chair
Haiyan Tian
Committee Chair School
Mathematics and Natural Sciences
Committee Member 2
James Lambers
Committee Member 2 School
Mathematics and Natural Sciences
Committee Member 3
Huiqing Zhu
Committee Member 3 School
Mathematics and Natural Sciences
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.
Copyright
Cyril Delanyo Ocloo, 2020
Recommended Citation
Ocloo, Cyril, "A Time Integration Method of Approximate Particular Solutions for Nonlinear Ordinary Differential Equations" (2020). Master's Theses. 729.
https://aquila.usm.edu/masters_theses/729
Included in
Numerical Analysis and Computation Commons, Ordinary Differential Equations and Applied Dynamics Commons, Other Applied Mathematics Commons, Partial Differential Equations Commons