Help: Adaptive Runge-Kutta

This is the ODEINT algorithm from "Numerical Recipes in Pascal" by W.H. Press, B.P. Flannery, S.A. Teukolsky and W.T. Vetterling, Cambridge U. Press, Cambridge 1989 (with a few minor changes). The algorithm uses fourth-order Runge-Kutta together with step doubling and Richardson extrapolation to obtain a fifth-order method. The step size is adjusted to achieve a given error tolerance.

Let Y₁ be the result of one fourth-order Runge-Kutta step of step size h starting at (X,Y), and Y₂ the result of two fourth-order Runge-Kutta steps of size h/2 starting from the same point. Then we take

Y(X + h) = (16 Y₂ - Y₁)/15

with local error estimate Y₂ - Y₁. We adjust h so that

|Y₂ - Y₁| < p |Y|

where p is the "Error tolerance" as set in the Main window.

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