## Abstract

We develop a two-dimensional adaptive pseudo-spectral procedure which is capable of improving the approximation of functions which are rapidly varying in two dimensions. The method is based on introducing two-dimensional coordinate transformations chosen to minimize certain functionals of the solution to be approximated. The method is illustrated by numerical computation of the solutions to a system of reaction diffusion equations modeling the gasless combustion of a solid fuel. Spatio-temporal patterns are computed as a parameter μ, related to the activation energy, is increased above a critical value μ_{c}. The spatial patterns are characterized by a very rapid variation in the direction of the axis of the cylinder, together with a standing wave pattern in the direction of the azimuthal angle ψ For small values of μ - μ_{c} the solutions exhibit a nearly sinusoidal dependence in both time and ψ As μ is increased further relaxation oscillations in both time and ψ occur. Beyond a critical value of μ stable time-periodic solutions are no longer found and the solution exhibits a quasi-periodic time dependence.

Original language | English (US) |
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Pages (from-to) | 174-196 |

Number of pages | 23 |

Journal | Journal of Computational Physics |

Volume | 91 |

Issue number | 1 |

DOIs | |

State | Published - Nov 1990 |

## ASJC Scopus subject areas

- Numerical Analysis
- Modeling and Simulation
- Physics and Astronomy (miscellaneous)
- General Physics and Astronomy
- Computer Science Applications
- Computational Mathematics
- Applied Mathematics