Extrapolation of symplectic methods for Hamiltonian problems

Applied Numerical Mathematics

Volumn 34, Issue 2, 2000, Pages 189-205

  Chan, R P K ^a   Murua, A ^b  

^a Department of Mathematics   (New Zealand)

^b UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; ERROR ANALYSIS; INTEGRATION; PROBLEM SOLVING; RUNGE KUTTA METHODS;

HAMILTONIAN PROBLEMS; LINEAR ERROR GROWTH; SYMPLECTIC METHODS;

EXTRAPOLATION;

EID: 0034227591     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(99)00127-0     Document Type: Article

References (14)

1. [1] G. Bader, P. Deuflhard, A semi-implicit midpoint rule for stiff systems of ordinary differential equations, Numer. Math. 41 (1983) 373-398.
2. [2] S. Blanes, F. Casas, J. Ros, Extrapolation of symplectic integrators, Celestial Mech., submitted.
3. [3] R. Bulirsch, J. Stoer, Numerical treatment of ordinary differential equations by extrapolation methods, Numer. Math. 8 (1966) 1-13.
4. [4] M.P. Calvo, E. Hairer, Accurate long-term integration of dynamical systems, Appl. Numer. Math. 18 (1995) 95-105.
5. [5] R. Frank, J. Schneid, C.W. Ueberhuber, The concept of B-convergence, SIAM J. Numer. Anal. 18 (1981) 753-780.
6. [6] W.B. Gragg, On extrapolation algorithms for ordinary initial value problems, SIAM J. Numer. Anal. 2 (1965) 384-403.
7. [7] E. Hairer, Ch. Lubich, Asymptotic expansions of the global error of fixed-stepsize methods, Numer. Math. 45 (1984) 345-360.
8. [8] E. Hairer, S.P. Nørsett, G. Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, 2nd Revised Edition, Springer Series in Computational Mathematics, Vol. 8, Springer, Berlin, 1993.
9. [9] B. Lindberg, On smoothing and extrapolation for the trapezoidal rule, BIT 11 (1971) 29-52.
10. [10] B. Lindberg, IMPEX 2 - a procedure for solution of systems of stiff differential equations, Report TRITA-NA-7303, Dept. of Inf. Proc. Comp. Sci., Roy. Inst. Tech., Stockholm.
11. [11] A. Prothero, A. Robinson, On the stability and accuracy of one-step methods for solving stiff systems of ordinary differential equations, Math. Comp. 28 (1974) 145-162.
12. [12] L.F. Richardson, The deferred approach to the limit, Phil. Trans. A 226 (1927) 299-349.
13. [13] W. Romberg, Vereinfachte numerische Integration, Norske Vid. Selsk. Forhdl. 28 (1955) 30-36.
14. [14] H.J. Stetter, Asymptotic expansions for the error of discretization algorithms for non-linear functional equations, Numer. Math. 7 (1965) 18-31.