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References
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P. J. Channell, Symplectic integration algorithms, Los Alamos National Laboratory Rep. AT-6:ATN 83-9 (1983).
- F. M. Lasagni, Canonical Runge-Kutta methods, Z. Angew. Math. Phys. 39 (1988), no. 6, 952–953. MR 973194, DOI 10.1007/BF00945133
- Roger Penrose, The emperor’s new mind, The Clarendon Press, Oxford University Press, New York, 1989. Concerning computers, minds, and the laws of physics; With a foreword by Martin Gardner. MR 1048125, DOI 10.1093/oso/9780198519737.001.0001 R. D. Ruth, A canonical integration technique, IEEE Trans. Nucl. Sci. 30 (1983), 2669-2671.
- J. M. Sanz-Serna, Runge-Kutta schemes for Hamiltonian systems, BIT 28 (1988), no. 4, 877–883. MR 972812, DOI 10.1007/BF01954907
- J. M. Sanz-Serna, Symplectic integrators for Hamiltonian problems: an overview, Acta numerica, 1992, Acta Numer., Cambridge Univ. Press, Cambridge, 1992, pp. 243–286. MR 1165727, DOI 10.1017/s0962492900002282
- Yu. B. Suris, Preservation of symplectic structure in the numerical solution of Hamiltonian systems, Numerical solution of ordinary differential equations (Russian), Akad. Nauk SSSR, Inst. Prikl. Mat., Moscow, 1988, pp. 148–160, 232, 238–239 (Russian, with English summary). MR 1115223 E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorensen, LAPACK users’ guide, SIAM, Philadelphia, PA, 1992. J. J. Dongarra, J. R. Bunch, C. B. Moler, and G. W. Stewart, LINPACK users’ guide, SIAM, Philadelphia, PA, 1979.
- B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow, Y. Ikebe, V. C. Klema, and C. B. Moler, Matrix eigensystem routines—EISPACK guide, 2nd ed., Lecture Notes in Computer Science, Vol. 6, Springer-Verlag, Berlin-New York, 1976. MR 0494879, DOI 10.1007/3-540-07546-1
- Handbook for automatic computation. Vol. II, Die Grundlehren der mathematischen Wissenschaften, Band 186, Springer-Verlag, New York-Heidelberg, 1971. Linear algebra; Compiled by J. H. Wilkinson and C. Reinsch. MR 0461856
- K. O. Geddes, S. R. Czapor, and G. Labahn, Algorithms for computer algebra, Kluwer Academic Publishers, Boston, MA, 1992. MR 1256483, DOI 10.1007/b102438
Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Math. Comp. 64 (1995), 1341-1354
- DOI: https://doi.org/10.1090/S0025-5718-95-99724-5