Date of Award

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.

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