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Problem
Given the IVP
y(a) = y0
approximate y(t) with an error less than εabs.
Assumptions
The function f(t, y) should be continuous in both variables.
Tools
We will use a variation of the Runge-Kutta-Fehlberg method to find two approximations of the value y(t1) to find an optimal value of h.
Initial Conditions
Set h = t1 − t0. Let y1 be the approximation of y(t1).
Process
Define
K0 = f( y0, t0 )
K1 = f( y0 + ½ h K0, t0 + ½ h )
K2 = f( y0 + ½ h K1, t0 + ½ h )
K3 = f( y0 + h K2, t0 + h )
Then let
Copyright ©2006 by Douglas Wilhelm Harder. All rights reserved.