HTML version of Scripted Foils prepared 28 December 1996

Foil 22 Definition of Multi-step methods

From CPS615-Discussion of Ordinary Differential Equations and Start of Parallel N-Body Algorithm Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 10 October 96. by Geoffrey C. Fox *
Secs 303.8
1 The predictor/corrector methods use previous values Xi-1, Xi-2, ...... to increase accuracy p - not extra values between Xi and Xi+1 as in Runge Kutta
2 General form of multi-step difference equation:
3 Xi+1 = am-1Xi + am-2 Xi-1 + ..... + a0Xi+1-m + h(bmf(ti+1, Xi+1) + bm-1 f (ti, Xi) + .....
  • + b0f(ti+1-m, Xi+1-m)))
4 if coefficient of f evaluation dependent on ti+1 bm=0, this is an explicit equation
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