RKN1210 12th/10th order Runge-Kutta-Nystrom integrator
RKN1210() is a 12th/10th order numerical integrator for ordinary differential equations of the form
y'' = f(t, y) (1)
with initial conditions
y(t0) = y0, y'(t0) = yp0 (2)
This second-order differential equation is integrated with a
Runge-Kutta-Nystrom method, with 17 function evaluations per step. The RKN-class of integrators is especially suited for this purpose, since compared to a classic Runge-Kutta integration scheme the same accuracy can be obtained with less function evaluations.
This RKN12(10) method is a very high-order method, to be used in problems with *extremely* stringent error tolerances. In verious studies, it has been shown that this particular integration technique is overall more efficient for ODE's of the form (1) than multi-step or extrapolation methods that give the same accuracy.
RKN1210's behavior is very similar MATLAB's ODE-integrator suite; you can set options via ODESET, and input and output values are also practically the same.
Both output functions and event functions are fully supported.
The construction of RKN12(10) is described in
High-Order Embedded Runge-Kutta-Nystrom Formulae
J. R. DORMAND, M. E. A. EL-MIKKAWY, AND P. J. PRINCE
IMA Journal of Numerical Analysis (1987) 7, 423-430
Coefficients obtained from
http://www.tampa.phys.ucl.ac.uk/rmat/test/rknint.f
These are also available in any format on request to these authors.
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