Date of Award
Fall 2019
Degree Type
Masters Thesis
Degree Name
Master of Science (MS)
School
Mathematics and Natural Sciences
Committee Chair
C.S. Chen
Committee Chair School
Mathematics and Natural Sciences
Committee Member 2
James Lambers
Committee Member 2 School
Mathematics and Natural Sciences
Committee Member 3
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.
Copyright
2019, Lionel Amuzu
Recommended Citation
Amuzu, Lionel, "Localized Method of Approximate Particular Solutions for Solving Fourth-Order PDEs" (2019). Master's Theses. 683.
https://aquila.usm.edu/masters_theses/683