dopri45
DOPRI45
Dormand-Prince method
In numerical analysis, the Dormand–Prince method or DOPRI method, is an embedded method for solving ordinary differential equations (Dormand & Prince 1980). The method is a member of the Runge–Kutta family of ODE solvers. More specifically, it uses six function evaluations to calculate fourth- and fifth-order accurate solutions.
Applicable for non-stiff problems of medium accuracy.
The Butcher tableau for the adaptive Dormand–Prince method is:
| 0 | |||||||
| 1/5 | 1/5 | ||||||
| 3/10 | 3/40 | 9/40 | |||||
| 4/5 | 44/45 | -56/15 | 32/9 | ||||
| 8/9 | 19372/6561 | -25360/2187 | 64448/6561 | -212/729 | |||
| 1 | 9017/3168 | -355/33 | 46732/5247 | 49/176 | −5103/18656 | ||
| 1 | 35/384 | 0 | 500/1113 | 125/192 | −2187/6784 | 11/84 | |
| 35/384 | 0 | 500/1113 | 125/192 | −2187/6784 | 11/84 | 0 | |
| 5179/57600 | 0 | 7571/16695 | 393/640 | −92097/339200 | 187/2100 | 1/40 |
The first row of b coefficients gives the fifth-order accurate solution, and the second row gives the fourth-order accurate solution.
Applicable solver settings:
- Absolute tolerance
- Relative tolerance
- Initial step size
- Max step size
- Min step size
- Refine
- Limit data points to last
- Norm Control
- Allowed step size violations
- Enable saturation
Reference
- Dormand, J. R. and P. J. Prince, “A family of embedded Runge-Kutta formulae,” J. Comp. Appl. Math., Vol. 6, 1980, pp 19-26.
dopri45.txt · Last modified: 2023/04/05 14:33 by daria
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