Fourth-order 2N-storage Runge-Kutta schemes
作者： Christopher A. Kennedy , Mark H. Carpenter
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摘要: A family of five-stage fourth-order Runge-Kutta schemes is derived; these required only two storage locations. particular scheme identified that has desirable efficiency characteristics for hyperbolic and parabolic initial (boundary) value problems. This competitive with the classical method (high-storage) considerably more efficient accurate than existing third-order low-storage schemes.
jaxa.jp参考文章(8)
P. W. Sharp, E. Smart, Explicit Runge-Kutta pairs with one more derivative evaluation than the minimum SIAM Journal on Scientific Computing. ,vol. 14, pp. 338- 348 ,(1993) , 10.1137/0914021
J.H Williamson, Low-storage Runge-Kutta schemes Journal of Computational Physics. ,vol. 35, pp. 48- 56 ,(1980) , 10.1016/0021-9991(80)90033-9
Kenneth R. Jackson, J. C. Butcher, The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods Mathematics of Computation. ,vol. 51, pp. 377- ,(1987) , 10.2307/2008600
Robert D. Skeel, Thirteen ways to estimate global error Numerische Mathematik. ,vol. 48, pp. 1- 20 ,(1986) , 10.1007/BF01389440
Mark H Carpenter, David Gottlieb, Saul Abarbanel, Wai-Sun Don, None, The Theoretical Accuracy of Runge–Kutta Time Discretizations for the Initial Boundary Value Problem: A Study of the Boundary Error SIAM Journal on Scientific Computing. ,vol. 16, pp. 1241- 1252 ,(1995) , 10.1137/0916072
David J. Fyfe, Economical evaluation of Runge-Kutta formulae Mathematics of Computation. ,vol. 20, pp. 392- 398 ,(1966) , 10.1090/S0025-5718-1966-0202317-0
J. H. Verner, Explicit Runge–Kutta Methods with Estimates of the Local Truncation Error SIAM Journal on Numerical Analysis. ,vol. 15, pp. 772- 790 ,(1978) , 10.1137/0715051
J.R. Dormand, P.J. Prince, A family of embedded Runge-Kutta formulae Journal of Computational and Applied Mathematics. ,vol. 6, pp. 19- 26 ,(1980) , 10.1016/0771-050X(80)90013-3