Convergence Analysis of Krylov Subspace Spectral Methods for Reaction-Diffusion Equations
Document Type
Article
Publication Date
9-6-2018
Department
Mathematics
School
Mathematics and Natural Sciences
Abstract
Krylov subspace spectral (KSS) methods are explicit time-stepping methods for partial differential equations that are designed to extend the advantages of Fourier spectral methods, when applied to constant-coefficient problems, to the variable-coefficient case. This paper presents a convergence analysis of a first-order KSS method applied to a system of coupled equations for modeling first-order photobleaching kinetics. The analysis confirms what has been observed in numerical experiments—that the method is unconditionally stable and achieves spectral accuracy in space. Further analysis shows that this unconditional stability is not limited to the case in which the leading coefficient is constant.
Publication Title
Journal of Scientific Computing
First Page
1
Last Page
22
Recommended Citation
Sheikholeslami, S.,
Lambers, J. V.,
Walker, C.
(2018). Convergence Analysis of Krylov Subspace Spectral Methods for Reaction-Diffusion Equations. Journal of Scientific Computing, 1-22.
Available at: https://aquila.usm.edu/fac_pubs/15772