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


Updated 20 Feb 2004

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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/

Cite As

Charalampos Tsitouras (2023). rkn86 (https://www.mathworks.com/matlabcentral/fileexchange/3153-rkn86), MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R13
Compatible with any release
Platform Compatibility
Windows macOS Linux
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Version Published Release Notes

In the function call there is the update of time t in the inner stages missing.
It should be
f(:,j)=feval(..., t+alpha(j)*h, ...);
and not
f(:,j)=feval(..., t, ...);