# Computer algebra derives discretisations of the stochastically forced Burgers' partial differential equation

Technical report

*Computer algebra derives discretisations of the stochastically forced Burgers' partial differential equation.*Toowoomba, Australia. University of Southern Queensland.

Title | Computer algebra derives discretisations of the stochastically forced Burgers' partial differential equation |
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Report Type | Technical report |

Authors | |

Author | Roberts, A. J. |

Institution of Origin | University of Southern Queensland |

Number of Pages | 31 |

Year | 2006 |

Publisher | University of Southern Queensland |

Place of Publication | Toowoomba, Australia |

Abstract | [Abstract]: The computer algebra routine documented here empowers you to reproduce and check many of the details described elsewhere. We consider a region of a spatial domain far from any boundaries, and apply stochastic centre manifold techniques to derive a discrete model for the dynamics. The approach automatically parametrises the microscale structures induced by spatially varying stochastic noise within each element. The crucial aspect of this work is that we explore how many noise processes and neighbouring elements may interact in nonlinear dynamics. |

Keywords | computer algebra, Burgers' partial differential equation, stochastic analysis |

ANZSRC Field of Research 2020 | 490409. Ordinary differential equations, difference equations and dynamical systems |

490302. Numerical analysis | |

490510. Stochastic analysis and modelling | |

Public Notes | File reproduced in accordance with the copyright policy of the publisher/author. |

Byline Affiliations | Department of Mathematics and Computing |

https://research.usq.edu.au/item/9xx2z/computer-algebra-derives-discretisations-of-the-stochastically-forced-burgers-partial-differential-equation

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