Krylov Subspace Spectral Methods with Non-homogenous Boundary Conditions

<p>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.</p>

Name thesis:degree_name

Master of Science (MS)

Level thesis:degree_level

Masters Thesis

Year dc:date.available

2019

Author dc:creator

• Hendley, Abbie

Contributors dc:contributor

• James Lambers
• Haiyan Tian
• Huiqing Zhu

• partial differential equation
• numerical
• Fast Fourier Transform
• Dirichlet
• analysis
• Numerical Analysis and Computation
• Numerical Analysis and Scientific Computing
• Partial Differential Equations

Repository record dc:identifier

https://aquila.usm.edu/masters_theses/674

OAI identifier oai:identifier

oai:aquila.usm.edu:masters_theses-1728