Date of Award
Summer 8-2011
Degree Type
Masters Thesis
Degree Name
Master of Science (MS)
Department
Mathematics
Committee Chair
Haiyan Tan
Committee Chair Department
Mathematics
Committee Member 2
Joseph Kolibal
Committee Member 2 Department
Mathematics
Committee Member 3
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.
Copyright
2011, Megan LaShea Richardson
Recommended Citation
Richardson, Megan LaShea, "A Comparison of Two Different Methods for Solving Biharmonic Boundary Valve Problems" (2011). Master's Theses. 213.
https://aquila.usm.edu/masters_theses/213