Spectral algorithms for reaction-diffusion equations

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Title: Spectral algorithms for reaction-diffusion equations
Authors: Craster, RV
Sassi, R
Item Type: Working Paper
Abstract: A collection of codes (in MATLAB & Fortran 77), and examples, for solving reaction-diffusion equations in one and two space dimensions is presented. In areas of the mathematical community spectral methods are used to remove the stiffness associated with the diffusive terms in a reaction-diffusion model allowing explicit high order timestepping to be used. This is particularly valuable for two (and higher) space dimension problems. Our aim here is to provide codes, together with examples, to allow practioners to easily utilize, understand and implement these ideas; we incorporate recent theoretical advances such as exponential time differencing methods and provide timings and error comparisons with other more standard approaches. The examples are chosen from the literature to illustrate points and queries that naturally arise.
Issue Date: 17-Oct-2018
URI: http://hdl.handle.net/10044/1/63929
Publisher: arXiv
Copyright Statement: © 2006 Universita degli studi di Milano, Polo didattico e di ricerca di Crema. Licensed under a Creative Commons Attribution 4.0 International licence (CC BY 4.0 - https://creativecommons.org/licenses/by/4.0/)
Keywords: math.NA
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences

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