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Regarding the absolute stability of Størmer-Cowell methods
| 1. | Dept. of Mathematical Sciences, NTNU Trondheim, N-7491 Trondheim, Norway |
| 2. | Dept. Computer Science, University of Leuven, Belgium, BE-3001 Heverlee |
References:
| [1] |
G. Dahlquist, On accuracy and unconditional stability of linear multistep methods for second order differential equations, BIT; Nordisk Tidskrift for Informationsbehandling (BIT), 18 (1978), 133-136.
doi: 10.1007/BF01931689. |
| [2] |
W. Gautschi, Numerical integration of ordinary differential equations based on trigonometric polynomials, Numerische Mathematik, 3 (1961), 381-397.
doi: 10.1007/BF01386037. |
| [3] |
K. Grazier, W. Newman, J. Hyman, P. Sharp and D. Goldstein, Achieving Brouwer's law with high-order Störmer multistep methods, ANZIAM J., 46 (2004/05), C786–-C804. |
| [4] |
E. Hairer, C. Lubich and G. Wanner, Geometric numerical integration illustrated by the Störmer-Verlet method, Acta Numerica, 12 (2003), 399-450.
doi: 10.1017/S0962492902000144. |
| [5] |
E. Hairer, S. Nørsett and G. Wanner, "Solving Ordinary Differential Equations: Nonstiff Problems, vol. 1," Springer Verlag, 1993. |
| [6] |
E. Hairer and G. Wanner, "Solving Ordinary Differential Equations {II}: Stiff and Differential-Algebraic Problems, vol. 2," Springer, 2004. |
| [7] |
P. Henrici, "Discrete Variable Methods in Ordinary Differential Equations, vol. 1," New York: Wiley, 1962. |
| [8] |
J. Lambert, "Computational Methods in Ordinary Differential Equations," Wiley New York, 1973. |
| [9] |
J. Lambert and I. Watson, Symmetric multistip methods for periodic initial value problems, IMA Journal of Applied Mathematics, 18 (1976), 189-202.
doi: 10.1093/imamat/18.2.189. |
| [10] |
W. I. Newman, F. Varadi, A. Y. Lee, W. M. Kaula, K. R. Grazier and J. M. Hyman, Numerical integration, Lyapunov exponents and the outer Solar System, Bulletin of the American Astronomical Society, 32 (2000), 859. |
| [11] |
G. Quinlan and S. Tremaine, Symmetric multistep methods for the numerical integration of planetary orbits, The Astronomical Journal, 100 (1990), 1694-1700. |
| [12] |
P. Sharp, Comparisons of high order stormer and explicit Runge-kutta Nyström methods for N-body simulations of the solar system, Tech. Rep., Department of Mathematics, The University of Auckland, New Zealand, (2000). |
| [13] |
E. Stiefel and D. G. Bettis, Stabilization of Cowell's method, Numerische Mathematik, 13 (1969), 154-175.
doi: 10.1007/BF02163234. |
| [14] |
E. Thorbergsen, "Undersøkelse av Noen Metoder for Baneproblemer," Master's thesis, Norges Tekniske Høyskole(NTH), Trondheim, Norway, 1976. |
| [15] |
F. Varadi and B. Runnegar, Successive refinements in long-term integrations of planetary orbits, The Astrophysical Journal, 592 (2003), 620-630. |
show all references
References:
| [1] |
G. Dahlquist, On accuracy and unconditional stability of linear multistep methods for second order differential equations, BIT; Nordisk Tidskrift for Informationsbehandling (BIT), 18 (1978), 133-136.
doi: 10.1007/BF01931689. |
| [2] |
W. Gautschi, Numerical integration of ordinary differential equations based on trigonometric polynomials, Numerische Mathematik, 3 (1961), 381-397.
doi: 10.1007/BF01386037. |
| [3] |
K. Grazier, W. Newman, J. Hyman, P. Sharp and D. Goldstein, Achieving Brouwer's law with high-order Störmer multistep methods, ANZIAM J., 46 (2004/05), C786–-C804. |
| [4] |
E. Hairer, C. Lubich and G. Wanner, Geometric numerical integration illustrated by the Störmer-Verlet method, Acta Numerica, 12 (2003), 399-450.
doi: 10.1017/S0962492902000144. |
| [5] |
E. Hairer, S. Nørsett and G. Wanner, "Solving Ordinary Differential Equations: Nonstiff Problems, vol. 1," Springer Verlag, 1993. |
| [6] |
E. Hairer and G. Wanner, "Solving Ordinary Differential Equations {II}: Stiff and Differential-Algebraic Problems, vol. 2," Springer, 2004. |
| [7] |
P. Henrici, "Discrete Variable Methods in Ordinary Differential Equations, vol. 1," New York: Wiley, 1962. |
| [8] |
J. Lambert, "Computational Methods in Ordinary Differential Equations," Wiley New York, 1973. |
| [9] |
J. Lambert and I. Watson, Symmetric multistip methods for periodic initial value problems, IMA Journal of Applied Mathematics, 18 (1976), 189-202.
doi: 10.1093/imamat/18.2.189. |
| [10] |
W. I. Newman, F. Varadi, A. Y. Lee, W. M. Kaula, K. R. Grazier and J. M. Hyman, Numerical integration, Lyapunov exponents and the outer Solar System, Bulletin of the American Astronomical Society, 32 (2000), 859. |
| [11] |
G. Quinlan and S. Tremaine, Symmetric multistep methods for the numerical integration of planetary orbits, The Astronomical Journal, 100 (1990), 1694-1700. |
| [12] |
P. Sharp, Comparisons of high order stormer and explicit Runge-kutta Nyström methods for N-body simulations of the solar system, Tech. Rep., Department of Mathematics, The University of Auckland, New Zealand, (2000). |
| [13] |
E. Stiefel and D. G. Bettis, Stabilization of Cowell's method, Numerische Mathematik, 13 (1969), 154-175.
doi: 10.1007/BF02163234. |
| [14] |
E. Thorbergsen, "Undersøkelse av Noen Metoder for Baneproblemer," Master's thesis, Norges Tekniske Høyskole(NTH), Trondheim, Norway, 1976. |
| [15] |
F. Varadi and B. Runnegar, Successive refinements in long-term integrations of planetary orbits, The Astrophysical Journal, 592 (2003), 620-630. |
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