HTML version of Scripted Foils prepared 28 December 1996

Foil 18 The Classical Runge-Kutta -- In Words

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 253.4
1 Runge Kutta methods achieve better results than Euler by using intermediate computations at intermediate time values
2 The fourth-order rule is the favorite method as it achieves good accuracy with modest computational complexity -- the algorithm is in words:
3 Use derivative of first time step to get trial midpoint
4 Use its derivative at first time step to get second trial midpoint
5 Use its derivative to get a trial end point
6 Integrate by Simpon's Rule, using average of two midpoint estimates
7 Global error is fourth order
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