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

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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.

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Authors and Affiliations

  1. Department of Radiation Oncology, Beaumont Health, Royal Oak, MI, 48073, USA

    Somayyeh Sheikholeslami

  2. School of Mathematics and Natural Sciences, The University of Southern Mississippi, 118 College Dr #5043, Hattiesburg, MS, 39406, USA

    James V. Lambers & Carley Walker

Authors
  1. Somayyeh Sheikholeslami
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  2. James V. Lambers
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  3. Carley Walker
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Correspondence to James V. Lambers.

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Sheikholeslami, S., Lambers, J.V. & Walker, C. Convergence Analysis of Krylov Subspace Spectral Methods for Reaction–Diffusion Equations. J Sci Comput 78, 1768–1789 (2019). https://doi.org/10.1007/s10915-018-0824-5

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  • DOI: https://doi.org/10.1007/s10915-018-0824-5

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