## Abstract

Detailed microscale simulation is typically too computationally ex- pensive for the long time simulations necessary to explore macroscale dynamics. Projective integration uses bursts of the microscale simula- tor, on microscale time steps, and then computes an approximation to the system over a macroscale time step by extrapolation. Projective integration has the potential to be an effective method to compute the long time dynamic behaviour of multiscale systems. However, many multiscale systems are significantly in influenced by noise. By a maximum likelihood estimation, we fit a linear stochastic differential equation to short bursts of data. The analytic solution of the linear stochastic differential equation then estimates the solution over a macroscale, projective integration, time step. We explore how the noise affects the projective integration in two different methods. Monte Carlo simula- tion suggests design parameters offering stability and accuracy for the algorithms. The algorithms developed here may be applied to compute the long time dynamic behaviour of multiscale systems with noise and to exploit parallel computation.

Original language | English (US) |
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Pages (from-to) | C661-C677 |

Journal | ANZIAM Journal |

Volume | 52 |

State | Published - 2010 |

## All Science Journal Classification (ASJC) codes

- Mathematics (miscellaneous)