Date of Award
Summer 2019
Degree Type
Masters Thesis
Degree Name
Master of Science (MS)
School
Mathematics and Natural Sciences
Committee Chair
James Lambers
Committee Chair School
Mathematics and Natural Sciences
Committee Member 2
Haiyan Tian
Committee Member 2 School
Mathematics and Natural Sciences
Committee Member 3
Huiqing Zhu
Committee Member 3 School
Mathematics and Natural Sciences
Abstract
For this thesis, Krylov Subspace Spectral (KSS) methods, developed by Dr. James Lambers, will be used to solve a one-dimensional, heat equation with non-homogenous boundary conditions. While current methods such as Finite Difference are able to carry out these computations efficiently, their accuracy and scalability can be improved. We will solve the heat equation in one-dimension with two cases to observe the behaviors of the errors using KSS methods. The first case will implement KSS methods with trigonometric initial conditions, then another case where the initial conditions are polynomial functions. We will also look at both the time-independent and time-dependent cases for both sets of initial conditions for discrepancies in accuracy and efficiency. Our numerical results will be compared to the results given by Finite Difference methods to show that accuracy can be improved without sacrificing efficiency.
Copyright
2019, Abbie Hendley
Recommended Citation
Hendley, Abbie, "Krylov Subspace Spectral Methods with Non-homogenous Boundary Conditions" (2019). Master's Theses. 674.
https://aquila.usm.edu/masters_theses/674
Included in
Analysis Commons, Numerical Analysis and Computation Commons, Numerical Analysis and Scientific Computing Commons, Partial Differential Equations Commons