Journal of Scientific Computing

, Volume 78, Issue 3, pp 1768–1789 | Cite as

Convergence Analysis of Krylov Subspace Spectral Methods for Reaction–Diffusion Equations

  • Somayyeh Sheikholeslami
  • James V. LambersEmail author
  • Carley Walker


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.


Lanczos algorithm Spectral methods Gauss quadrature FRAP Photobleaching kinetics equation 


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Authors and Affiliations

  1. 1.Department of Radiation OncologyBeaumont HealthRoyal OakUSA
  2. 2.School of Mathematics and Natural SciencesThe University of Southern MississippiHattiesburgUSA

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