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.

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