Basic HTML version of Foils prepared February 25 2000

Foil 20 Runge-Kutta Methods: Modified Euler II

From Parallel Programming for Particle Dynamics Extra Foils Computational Science CPS615 -- Spring 2000 Semester. by Geoffrey C. Fox
1 Midpoint Method is ?1 = f(ti,X(ti)) ?2 = f(ti+0.5*h,X(ti+0.5*h)) Xi+1 = Xi + h * ?2
2 ti
3 ti+1
4 Xi = Yi
5 Exact Yi+1
6 ?2 Approximate Tangent at Midpoint
7 Approximate Tangent at Midpoint through ti
8 ?1 Tangent at ti
9 Midpoint Approximation Xi+1
10 Global Error is O(h2)) Second Order Method
in Table To:

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