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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A holistic finite difference approach models linear dynamics consistently
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by A. J. Roberts PDF
Math. Comp. 72 (2003), 247-262 Request permission

Abstract:

I prove that a centre manifold approach to creating finite difference models will consistently model linear dynamics as the grid spacing becomes small. Using such tools of dynamical systems theory gives new assurances about the quality of finite difference models under nonlinear and other perturbations on grids with finite spacing. For example, the linear advection-diffusion equation is found to be stably modelled for all advection speeds and all grid spacings. The theorems establish an extremely good form for the artificial internal boundary conditions that need to be introduced to apply centre manifold theory. When numerically solving nonlinear partial differential equations, this approach can be used to systematically derive finite difference models which automatically have excellent characteristics. Their good performance for finite grid spacing implies that fewer grid points may be used and consequently there will be less difficulties with stiff rapidly decaying modes in continuum problems.
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Additional Information
  • A. J. Roberts
  • Affiliation: Department of Mathematics and Computing, University of Southern Queensland, Toowoomba, Queensland 4352, Australia
  • Email: aroberts@usq.edu.au
  • Received by editor(s): April 6, 2000
  • Received by editor(s) in revised form: November 14, 2000
  • Published electronically: June 4, 2002
  • © Copyright 2002 American Mathematical Society
  • Journal: Math. Comp. 72 (2003), 247-262
  • MSC (2000): Primary 37L65, 65M20, 37L10, 65P40, 37M99
  • DOI: https://doi.org/10.1090/S0025-5718-02-01448-5
  • MathSciNet review: 1933820