# Computer algebra derives the slow manifold of patch or element dynamics on lattices in two dimensions

Technical report

*Computer algebra derives the slow manifold of patch or element dynamics on lattices in two dimensions.*Adelaide, Australia. University of Adelaide.

Title | Computer algebra derives the slow manifold of patch or element dynamics on lattices in two dimensions |
---|---|

Report Type | Technical report |

Authors | MacKenzie, Tony (Author) and Roberts, A. J. (Author) |

Institution of Origin | University of Adelaide |

Number of Pages | 26 |

Year | 2014 |

Publisher | University of Adelaide |

Place of Publication | Adelaide, Australia |

Web Address (URL) | http://arxiv.org/pdf/1102.2037v1.pdf |

Abstract | Developments in dynamical systems theory provides new support for the discretisation of pdes and other microscale systems. Here we explore the methodology applied to the gap-tooth scheme in the equation-free approach of Kevrekidis in two spatial dimensions. The algebraic detail is enormous so we detail computer algebra procedures to handle the enormity. However, modelling the dynamics on 2D spatial patches appears to require a mixed numerical and algebraic approach that is detailed in this report. Being based upon the computation of residuals, the procedures here may be simply adapted to a wide class of reaction-diffusion equations. |

ANZSRC Field of Research 2020 | 490302. Numerical analysis |

490105. Dynamical systems in applications | |

461399. Theory of computation not elsewhere classified | |

Public Notes | This publication is copyright. It may be reproduced in whole or in part for the purposes of study, research, or review, but is subject to the inclusion of an acknowledgment of the source. |

Byline Affiliations | Department of Mathematics and Computing |

University of Adelaide |

https://research.usq.edu.au/item/q1638/computer-algebra-derives-the-slow-manifold-of-patch-or-element-dynamics-on-lattices-in-two-dimensions

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