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
Midpoint Method is ?1 = f(ti,X(ti)) ?2 = f(ti+0.5*h,X(ti+0.5*h)) Xi+1 = Xi + h * ?2
ti
ti+1
Xi = Yi
Exact Yi+1
?2 Approximate Tangent at Midpoint
Approximate Tangent at Midpoint through ti
?1 Tangent at ti
Midpoint Approximation Xi+1
Global Error is O(h2)) Second Order Method

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