Symmetric linear multistep methods

BIT Numerical Mathematics

Volumn 46, Issue 3, 2006, Pages 515-524

  Hairer, Ernst ^a  

^a UNIVERSITY OF GENEVA   (Switzerland)

Author keywords

Backward error analysis; Growth parameter; Linear multistep method; Long term stability; Parasitic solution; Symmetry; Weak instability

Indexed keywords

EID: 33749034455     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10543-006-0066-z     Document Type: Article

References (11)

1. G. Dahlquist, Fehlerabschätzungen bei Differenzenmethoden zur numerischen Integration gewöhnlicher Differentialgleichungen, Z. Angew. Math. Mech., 31 (1951), pp. 239-240.
2. G. Dahlquist, Convergence and stability in the numerical integration of ordinary differential equations, Math. Scand., 4 (1956), pp. 33-53.
3. G. Dahlquist, Stability and error bounds in the numerical integration of ordinary differential equations, Trans. Royal Inst. Technol., vol. 130, Stockholm, Sweden, 1959.
4. G. Dahlquist, 33 years of numerical instability, part I, BIT, 25 (1985), pp. 188-204.
5. E. Faou, E. Hairer, and T.-L Pham, Energy conservation with non-symplectic methods: examples and counter-examples, BIT, 44 (2004), pp. 699-709.
6. E. Hairer, Backward error analysis for multistep methods, Numer. Math., 84 (1999), pp. 199-232.
7. E. Hairer and C. Lubich, Symmetric multistep methods over long times, Numer. Math., 97 (2004), pp. 699-723.
8. E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration, Structure-Preserving Algorithms for Ordinary Differential Equations, 2nd edn., Springer Series in Computational Mathematics 31, Springer, Berlin, 2006.
9. P. Henrici, Discrete Variable Methods in Ordinary Differential Equations, John Wiley & Sons Inc., New York, 1962.
10. J. D. Lambert and I. A. Watson, Symmetric multistep methods for periodic initial value problems, J. Inst. Math. Appl., 18 (1976), pp. 189-202.
11. G. D. Quinlan and S. Tremaine, Symmetric multistep methods for the numerical integraastion of planetary orbits, Astron. J., 100 (1990), pp. 1694-1700.