Runge-Kutta methods for linear ordinary differential equations

Applied Numerical Mathematics

Volumn 31, Issue 2, 1999, Pages 227-238

  Zingg, D W ^a   Chisholm, T T ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; FINITE VOLUME METHOD; INTEGRATION; MAXWELL EQUATIONS; ORDINARY DIFFERENTIAL EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; VECTORS;

LINEAR ORDINARY DIFFERENTIAL EQUATIONS; SPATIAL DISCRETIZATION;

RUNGE KUTTA METHODS;

EID: 0033207809     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(98)00129-9     Document Type: Article

References (20)

1. E.K. Blum, A modification of the Runge-Kutta fourth-order method, Math. Comp. 16 (1962) 176-187.
2. J.C. Butcher, The non-existence of ten stage eighth order explicit Runge-Kutta methods, BIT 25 (1985) 521-540.
3. J.C. Butcher, The Numerical Analysis of Ordinary Differential Equations (Wiley, New York, 1987).
4. M.H. Carpenter and C.A. Kennedy, Fourth-order 2N-storage Runge-kutta Schemes, NASA TM 109112 (June 1994).
5. W.H. Enright, The efficient solution of linear constant-coefficient systems of differential equations, Simulation 30 (1978) 129-133.
6. S. Gill, A process for the step-by-step integration of differential equations in an automatic digital computing machine, Proc. Cambridge Philos. Soc. 47 (1951) 96-108.
7. Z. Haras and S. Ta'Asan, Finite-difference schemes for long-time integration, J. Comput. Phys. 114 (1994) 265-279.
8. F.Q. Hu, M.y. Hussaini and J.L. Manthey, Low-dissipation and low-dispersion Runge-Kutta schemes for computational acoustics, J. Comput. Phys. 124 (1996) 177-191.
9. H. Jurgens and D.W. Zingg, Implementation of a high-accuracy finite-difference scheme for linear wave phenomena, Houston J. Math. (July 1996).
10. J.D. Lambert, Computational Methods in Ordinary Differential Equations (Wiley, New York, 1973).
11. E.N. Lorenz, An N-cycle time-differencing scheme for stepwise numerical integration, Monthly Weather Rev. 99 (1971) 644-648.
12. L. Randez, Optimizing the numerical integration of initial value problems in shooting methods for linear boundary value problems, SIAM J. Sci. Comput. 14 (1993) 860-871.
13. L.F. Shampine, Cheaper integration of linear systems, Simulation 20 (1973) 17.
14. L.F. Shampine, Solution of structured non-stiff ODEs, J. Comput. Appl. Math. 15 (1986) 293-300.
15. E.B. Shanks, Higher-order Approximations of Runge-Kutta Type, NASA TN D-2920 (September 1965).
16. J.H. Williamson, Low-storage Runge-Kutta schemes, J. Comput. Phys. 35 (1980) 48-56.
17. A.A. Wray, Minimal Storage Time Advancement Schemes for Spectral Methods, Manuscript, NASA Ames Research Center (unpublished).
18. D.W. Zingg, A review of high-order and optimized finite-difference methods for simulating linear wave phenomena, AIAA paper 97-2088, in: Proceedings of the 13th AIAA Computational Fluid Dynamics Conference, American Institute for Aeronautics and Astronautics (June 1997).
19. D.w. Zingg and H. Lomax, Some aspects of high-order numerical solutions of the linear convection equation with forced boundary conditions, AIAA paper 93-3381, in: Proceedings of the 11th AIAA Computational Fluid Dynamics Conference, American Institute for Aeronautics and Astronautics (June 1993).
20. D.W. Zingg, H. Lomax and H.M. Jurgens, High-accuracy finite-difference schemes for linear wave propagation, SIAM J. Sci. Comput. 17 (1996) 328-346.