Date of Award
Fall 2020
Degree Type
Masters Thesis
Degree Name
Master of Science (MS)
School
Mathematics and Natural Sciences
Committee Chair
Dr. James V. Lambers
Committee Chair School
Mathematics and Natural Sciences
Committee Member 2
Dr. Haiyan Tian
Committee Member 2 School
Mathematics and Natural Sciences
Committee Member 3
Dr. Huiqing Zhu
Committee Member 3 School
Mathematics and Natural Sciences
Abstract
Krylov subspace spectral (KSS) methods are high-order accurate, explicit time-stepping methods for partial differential equations (PDEs) that also possess the stability characteristic of implicit methods. Unlike other time-stepping approaches, KSS methods compute each Fourier coefficient of the solution from an individualized approximation of the solution operator of the PDE. As a result, KSS methods scale effectively to higher spatial resolution. This thesis will present a stability analysis of a first-order KSS method applied to the wave equation in inhomogeneous media.
Copyright
Bailey Rester 2020
Recommended Citation
Rester, Bailey, "Stability Analysis of Krylov Subspace Spectral Methods for the 1-D Wave Equation in Inhomogeneous Media" (2020). Master's Theses. 789.
https://aquila.usm.edu/masters_theses/789