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ドルマン=プリンス法

出典: フリー百科事典『ウィキペディア(Wikipedia)』

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

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  1. ^ 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.
  2. ^ Dormand, John R. (1996), Numerical Methods for Differential Equations: A Computational Approach, Boca Raton: en:CRC Press.
  3. ^ Deuflhard, P., & Bornemann, F. (2012). Scientific computing with ordinary differential equations. en:Springer Science & Business Media.
  4. ^ Shampine, Lawrence F. (1986), "Some Practical Runge-Kutta Formulas", en:Mathematics of Computation, 46 (173): 135–150.

外部リンク

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関連項目

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関連文献

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  • 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.