ドルマン＝プリンス法
ドルマン＝プリンス法 (Dormand-Prince method) はMATLAB/GNU Octaveにおいてode45として搭載されている常微分方程式の数値解法であり、ルンゲ＝クッタ法の一つである[1][2][3][4]。
出典
[編集]- ^ Dormand, J. R.; Prince, P. J. (1980), "A family of embedded Runge-Kutta formulae", en:Journal of Computational and Applied Mathematics, 6 (1): 19–26.
- ^ Dormand, John R. (1996), Numerical Methods for Differential Equations: A Computational Approach, Boca Raton: en:CRC Press.
- ^ Deuflhard, P., & Bornemann, F. (2012). Scientific computing with ordinary differential equations. en:Springer Science & Business Media.
- ^ Shampine, Lawrence F. (1986), "Some Practical Runge-Kutta Formulas", en:Mathematics of Computation, 46 (173): 135–150.
外部リンク
[編集]- ドルマン・プリンス法でvan der Pol方程式をExcel VBAで計算
- On Dormand-Prince Method (PDF)
- Runge Kutta Methods and the Dormand Prince Method - YouTube
- Ordinary Differential Equation Solvers ODE23 and ODE45, Posted by Cleve Moler, May 26, 2014 (MathWorksのブログ)
- ode45 (MathWorksのウェブサイト)
- docs
.scipy .org /doc /scipy /reference /generated /scipy .integrate .ode .html (Python・SciPyでの実装) - www
.unige .ch /~hairer /prog /nonstiff /dopri5 .f (FORTRANでの実装) - commons
.apache .org /proper /commons-math /javadocs /api-3 .0 /org /apache /commons /math3 /ode /nonstiff /DormandPrince853Integrator .html (Javaでの実装) - www
.boost .org /doc /libs /1 _53 _0 /libs /numeric /odeint /doc /html /boost /numeric /odeint /runge _kutta _dopri5 .html (C++での実装)
関連項目
[編集]関連文献
[編集]- Engstler, C., & Lubich, C. (1997). MUR8: a multirate extension of the eighth-order Dormand-Prince method. Applied numerical mathematics, 25(2-3), 185-192.
- Calvo, M., Montijano, J. I., & Randez, L. (1990). A fifth-order interpolant for the Dormand and Prince Runge-Kutta method. Journal of Computational and Applied Mathematics, 29(1), 91-100.
- Aristoff, J. M., Horwood, J. T., & Poore, A. B. (2014). Orbit and uncertainty propagation: a comparison of Gauss–Legendre-, Dormand–Prince-, and Chebyshev–Picard-based approaches. Celestial Mechanics and Dynamical Astronomy, 118(1), 13-28.
- Seen, W. M., Gobithaasan, R. U., & Miura, K. T. (2014, July). GPU acceleration of Runge Kutta-Fehlberg and its comparison with Dormand-Prince method. In AIP Conference Proceedings (Vol. 1605, No. 1, pp. 16-21). AIP.
- Jiménez, J. C., Sotolongo, A., & Sanchez-Bornot, J. M. (2014). Locally linearized Runge Kutta method of Dormand and Prince. Applied Mathematics and Computation, 247, 589-606.
- Olemskoi, I. V. (2005). A fifth-order five-stage embedded method of the Dormand–Prince type. Zhurnal Vychislitel'noi Matematikii Matematicheskoi Fiziki, 45(7), 1181-1191.
- Novikov, A. E. E., & Novikov, E. A. (2007). An algorithm of variable order and step based on stages of the Dormand-Prince method of the eighth order of accuracy. Vychislitel'nye metodyi programmirovanie, 8(4), 317-325.
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