Date of Award

Summer 8-2011

Degree Type

Masters Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

Committee Chair

Dr. Haiyan Tan

Committee Chair Department

Mathematics

Committee Member 2

Dr. Joseph Kolibal

Committee Member 2 Department

Mathematics

Committee Member 3

Dr. C.S. Chen

Committee Member 3 Department

Mathematics

Abstract

We use the methods of compactly supported radial basis functions (CS-RBFs) and Delta-shaped basis functions (DBFs) to obtain the numerical solution of a two-dimensional biharmonic boundary value problem. The biharmonic equation is difficult to solve due to its existing fourth order derivatives, besides it requires more than one boundary conditions on the same part of the boundary. In this thesis, we use either a one-level or a two-level technique for constructing the approximate solution in the context of Kansa’s collocation method. This thesis will compare the accuracy of the methods of CS-RBFs and DBFs when applied to the biharmonic boundary value problem. Both methods can be used on an irregular shaped domain. Numerical results show that the DBF approach is superior than that of the CS-RBF.

Included in

Mathematics Commons

Share

COinS