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Problem
Given the IVP
y(t0) = y0
approximate y(t1).
Assumptions
The function f(t, y) should be continuous in both variables.
Tools
We will use Taylor series.
Initial Conditions
Set h = t1 − t0. Let y1 be the approximation of y(t1).
Process
Define
K0 = f( t0, y0 )
K1 = f( t0 + ½ h, y0 + ½ h K0 )
K2 = f( t0 + ½ h, y0 + ½ h K1 )
K3 = f( t0 + h, y0 + h K2 )
Then let
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