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6993 results in Mathematical modeling and methods

Page 17 of 350

  • SLOW-BURNING INSTABILITIES OF DUFORT–FRANKEL FINITE DIFFERENCING

  • Part of
  • DAVID GALLOWAY, DAVID IVERS
  • Journal:
    The ANZIAM Journal / Volume 63 / Issue 1 / January 2021
    Published online by Cambridge University Press:
    30 April 2021, pp. 23-38

  • DuFort–Frankel averaging is a tactic to stabilize Richardson’s unstable three-level leapfrog timestepping scheme. By including the next time level in the right-hand-side evaluation, it is implicit, but it can be rearranged to give an explicit updating formula, thus apparently giving the best of both worlds. Textbooks prove unconditional stability for the heat equation, and extensive use on a variety of advection–diffusion equations has produced many useful results. Nonetheless, for some problems the scheme can fail in an interesting and surprising way, leading to instability at very long times. An analysis for a simple problem involving a pair of evolution equations that describe the spread of a rabies epidemic gives insight into how this occurs. An even simpler modified diffusion equation suffers from the same instability. Finally, the rabies problem is revisited and a stable method is found for a restricted range of parameter values, although no prescriptive recipe is known which selects this particular choice.

  • ANZ VOLUME 62 ISSUE 4 COVER AND FRONT MATTER

  • Journal:
    The ANZIAM Journal / Volume 62 / Issue 4 / October 2020
    Published online by Cambridge University Press:
    20 April 2021, pp. f1-f2
    • Article
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  • EDITORIAL: SPECIAL ISSUE CELEBRATING THE ACHIEVEMENTS OF PROFESSOR G. C. WAKE

  • MARK I. NELSON, RODNEY O. WEBER
  • Journal:
    The ANZIAM Journal / Volume 62 / Issue 4 / October 2020
    Published online by Cambridge University Press:
    20 April 2021, pp. 353-354
    • Article
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  • ANZ VOLUME 62 ISSUE 4 COVER AND BACK MATTER

  • Journal:
    The ANZIAM Journal / Volume 62 / Issue 4 / October 2020
    Published online by Cambridge University Press:
    20 April 2021, pp. b1-b5
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  • STOCHASTIC MODEL PREDICTIVE CONTROL FOR SPACECRAFT RENDEZVOUS AND DOCKING VIA A DISTRIBUTIONALLY ROBUST OPTIMIZATION APPROACH

  • Part of
  • ZUOXUN LI, KAI ZHANG
  • Journal:
    The ANZIAM Journal / Volume 63 / Issue 1 / January 2021
    Published online by Cambridge University Press:
    19 April 2021, pp. 39-57

  • A stochastic model predictive control (SMPC) algorithm is developed to solve the problem of three-dimensional spacecraft rendezvous and docking with unbounded disturbance. In particular, we only assume that the mean and variance information of the disturbance is available. In other words, the probability density function of the disturbance distribution is not fully known. Obstacle avoidance is considered during the rendezvous phase. Line-of-sight cone, attitude control bandwidth, and thrust direction constraints are considered during the docking phase. A distributionally robust optimization based algorithm is then proposed by reformulating the SMPC problem into a convex optimization problem. Numerical examples show that the proposed method improves the existing model predictive control based strategy and the robust model predictive control based strategy in the presence of disturbance.

Page 17 of 350