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

© Northeast Parallel Architectures Center, Syracuse University, npac@npac.syr.edu

If you have any comments about this server, send e-mail to webmaster@npac.syr.edu.

Page produced by wwwfoil on Fri Aug 15 1997