rkn86

Solves numerically a system of ODEs of the form d^2 y/ dx^2=f(x,y).

Description

rkn86 Integrates a special system of second order ordinary differential equations of the form
d^2 y/dx^2 = f(x,y), y(x0)=y0, y'(x0)=y'0
using an effectivelly 8-stages Runge-Kutta-Nystrom pair of orders 8 and 6.
The method advances using the higher order formula (using local extrapolation).
The results are expected to be better than ODE86 for all tolerances.

based on the code ODE86

The coefficients of the Runge-Kutta-Nystrom pair NEW8(6) are taken from
S. N. Papakostas and Ch. Tsitouras, "High phase-lag order Runge-Kutta and Nystrom pairs",
SIAM J. Sci. Comput. 21(1999) 747-763.

The error control is based on
Ch. Tsitouras and S. N. Papakostas, "Cheap Error Estimation for Runge-Kutta methods", SIAM J. Sci. Comput. 20(1999) 2067-2088.

tested for Matlab version 6.5
URL address: http://users.ntua.gr/tsitoura/

Acknowledgements

The author wishes to acknowledge the following in the creation of this submission:
ode86
This submission has inspired the following:
Vectorized N-Body Equation, RKN1210 - A 12th/10th order Runge-Kutta-Nystrom integrator

• MATLAB release: MATLAB 6.5 (R13)

[Rody Oldenhuis]

I discovered a bug; your error estimation scheme (the two deltas) is incorrect! Take a look at my RKN1210 integrator how to do it; it will significantly improve your integrator's performance.

Theoretically, if you copy-paste your coefficients into my integrator and adjust the for loop limits from 1:17 to 1:8 and pow=1/12 into pow=1/8, your integrator should inherit all the additional features that I implemented :) I haven't tried this, but I think it's worth a shot.