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Author (up) Jones, W.B.; O'Brien, J.J. url  doi
  Title Pseudo-spectral methods and linear instabilities in reaction-diffusion fronts Type $loc['typeJournal Article']
  Year 1996 Publication Chaos (Woodbury, N.Y.) Abbreviated Journal Chaos  
  Volume 6 Issue 2 Pages 219-228  
  Abstract We explore the application of a pseudo-spectral Fourier method to a set of reaction-diffusion equations and compare it with a second-order finite difference method. The prototype cubic autocatalytic reaction-diffusion model as discussed by Gray and Scott [Chem. Eng. Sci. 42, 307 (1987)] with a nonequilibrium constraint is adopted. In a spatial resolution study we find that the phase speeds of one-dimensional finite amplitude waves converge more rapidly for the spectral method than for the finite difference method. Furthermore, in two dimensions the symmetry preserving properties of the spectral method are shown to be superior to those of the finite difference method. In studies of plane/axisymmetric nonlinear waves a symmetry breaking linear instability is shown to occur and is one possible route for the formation of patterns from infinitesimal perturbations to finite amplitude waves in this set of reaction-diffusion equations. (c) 1996 American Institute of Physics.  
  Address Advanced Systems Division, Silicon Graphics Inc., Mountain View, California 94043-1389COAPS, Florida State University, Tallahassee, Florida 32306-3041  
  Corporate Author Thesis  
  Publisher Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 1054-1500 ISBN Medium  
  Area Expedition Conference  
  Funding PMID:12780250 Approved $loc['no']  
  Call Number COAPS @ mfield @ Serial 714  
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