rkn86

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

Version 1.0.0.0 (2,5 ko)
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20 fév. 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/

Citation pour cette source

Charalampos Tsitouras (2026). rkn86 (https://fr.mathworks.com/matlabcentral/fileexchange/3153-rkn86), MATLAB Central File Exchange. Extrait(e) le .

Remerciements

Inspiré par : ode86

A inspiré : Vectorized N-Body Equation

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En savoir plus sur Numerical Integration and Differential Equations dans Help Center et MATLAB Answers

Informations générales

Compatibilité avec les versions de MATLAB

  • Compatible avec toutes les versions

Plateformes compatibles

  • Windows
  • macOS
  • Linux
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Version Publié le Notes de version
1.0.0.0

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, ...);