Basic HTML version of Foils prepared 14 October 1997

Foil 23 Definition of Multi-step methods

From Fox Presentation Fall 1995 CPS615 Basic Simulation Track for Computational Science -- Fall Semester 95/96/97. by Nancy McCracken and Geoffrey C. Fox
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
General form of multi-step difference equation:
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)))
if coefficient of f evaluation independent on ti+1 bm=0, this is an explicit equation

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