rkn86

版本 1.0.0.0 (2.5 KB) 作者: Charalampos Tsitouras
Solves numerically a system of ODEs of the form d^2 y/ dx^2=f(x,y).
5.0
(1)
4.5K 次下载
更新时间 2004/2/20

无许可证

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/

引用格式

Charalampos Tsitouras (2024). rkn86 (https://www.mathworks.com/matlabcentral/fileexchange/3153-rkn86), MATLAB Central File Exchange. 检索时间: .

MATLAB 版本兼容性
创建方式 R13
兼容任何版本
平台兼容性
Windows macOS Linux
类别
在 Help Center 和 MATLAB Answers 中查找有关 Numerical Integration and Differential Equations 的更多信息
致谢

参考作品: ode86

启发作品: Vectorized N-Body Equation

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

版本 已发布 发行说明
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, ...);