Adaptive Method of Approximate Particular Solution for One-Dimensional Differential Equations

<p>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.</p>

Name thesis:degree_name

Master of Science (MS)

Level thesis:degree_level

Masters Thesis

Discipline thesis:degree_discipline

Mathematics

Year dc:date.available

2014

Author dc:creator

• Dong, Yichuan

Contributors dc:contributor

• Huiqing Zhu
• C.S. Chen
• Haiyan Tian

• Adaptive Method
• MAPS
• Boundary Value Problem
• Adaptive MAPS

Repository record dc:identifier

https://aquila.usm.edu/masters_theses/9

OAI identifier oai:identifier

oai:aquila.usm.edu:masters_theses-1008