Date of Award
Spring 5-2014
Degree Type
Masters Thesis
Degree Name
Master of Science (MS)
Department
Mathematics
Committee Chair
Huiqing Zhu
Committee Chair Department
Mathematics
Committee Member 2
C.S. Chen
Committee Member 2 Department
Mathematics
Committee Member 3
Haiyan Tian
Committee Member 3 Department
Mathematics
Abstract
An adaptive algorithm for the Method Approximate Particular Solution (MAPS) using radial basis functions for solving boundary value problems is discussed in this work. The goal of the adaptive algorithm is to construct an optimal collocation points distribution that gives the required accuracy with the smallest number of degrees of freedom. I proposed the formulation of the adaptive MAPS for second order boundary value problems in an arbitrary dimensional setting. Then I applied this method to three different boundary value problems in one-dimensional setting. The performance of the adaptive method has been demonstrated by numerical experiments.
Copyright
2014, Yichuan Dong
Recommended Citation
Dong, Yichuan, "Adaptive Method of Approximate Particular Solution for One-Dimensional Differential Equations" (2014). Master's Theses. 9.
https://aquila.usm.edu/masters_theses/9