Scripted HTML version of Foils prepared 28 December 1996

Foil 13 Relationship of Error to Computation

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 60.4
Whenever f satisfies certain smoothness conditions, there is always a sufficiently small step size h such that the difference between the real function value at ti and the approximation Xi+1 is less than some required error magnitude e. [Burden and Faires]
Euler's method: one computation of the derivative function f at each step.
Other methods require less computation in order to produce the specified error e.

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