High order embedded Runge-Kutta formulae
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Từ khóa
Tài liệu tham khảo
Dormand, 1980, A family of embedded Runge-Kutta formulae, J. of Computational and Applied Maths., 6, 19, 10.1016/0771-050X(80)90013-3
Prince, 1979, Runge-Kutta processes and global error estimation, Ph.D. Thesis
Shampine, 1976, Global error estimation for ordinary differential equations, ACM TOMS, 2, 172, 10.1145/355681.355687
Hull, 1972, Comparing numerical methods for ordinary differential equations, SIAM J. Numer. Anal., 9, 603, 10.1137/0709052
Fehlberg, 1968, Classical fifth, sixth, seventh and eighth order Runge-Kutta formulas with stepsize control, NASA TR R-287
Fehlberg, 1969, Low order classical Runge-Kutta formulas with stepsize control and their application to some heat transfer problems, NASA TR R-315
Dormand, 1978, New Runge-Kutta algorithms for numerical simulation in dynamical astronomy, Celestial Mechanics, 18, 223, 10.1007/BF01230162
Merson, 1957
Verner, 1978, Explicit Runge-Kutta methods with estimates of the local truncation error, SIAM J. of Numer. Anal., 15, 772, 10.1137/0715051
Butcher, 1964, On Runge-Kutta processes of high order, J. Australian Math. Soc., 4, 179, 10.1017/S1446788700023387
Cook, 1979, An algorithm to yield a compact rational approximation to a decimal fraction, Teesside Polytechnic Mathematical Report 79-9