Date of Award

Fall 2019

Degree Type

Masters Thesis

Degree Name

Master of Science (MS)

School

Mathematics and Natural Sciences

Committee Chair

Prof C.S Chen

Committee Chair School

Mathematics and Natural Sciences

Committee Member 2

Dr James Lambers

Committee Member 2 School

Mathematics and Natural Sciences

Committee Member 3

Dr Huiqing Zhu

Committee Member 3 School

Mathematics and Natural Sciences

Abstract

In the past, dealing with fourth-order partial differential equations using the Local Method was not reliable due to difficulties in solving them directly. An approach such as splitting these equations into two Poisson differential equations was adopted to alleviate such challenges. However, this has a limitation since it is only applicable to Dirichlet and Laplace boundary conditions. In this paper, we solve fourth-order PDEs directly using the LMAPS. The improvement on the accuracy of this method was as a result of the proposed distribution of boundary conditions to alternating boundary points. And, also the use of suitable shape parameter; calculated using LOOCV(Leave-One-Out-Cross-Validation) Algorithm. The effectiveness of this Method was evident when we compared the results from two numerical examples.

Share

COinS