VSVO multistep formulae adapted to perturbed second-order differential equations

Applied Mathematics Letters

Volumn 11, Issue 3, 1998, Pages 83-87

  Vigo Aguiar, J ^a   Ferrandiz J M ^b  

^a UNIVERSITY OF SALAMANCA   (Spain)

^b UNIVERSITY OF ALICANTE   (Spain)

Author keywords

Numerical integration of perturbed ODEs; Oscillatory solutions; Variable step size algorithms

Indexed keywords

EID: 0041783271     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(98)00037-8     Document Type: Article

References (14)

1. E. Stiefel and G. Scheifele, Linear and Regular Celestial Mechanics, Springer, Berlin, (1970).
2. J. Vigo-Aguiar, Mathematical methods for precise calculation of satellite orbits, Ph.D. Dissertation, University of Valladolid, (1993); (Spanish language, available from the author).
3. G. Denk, A new numerical method for the integration of highly oscillatory second-order ordinary differential equations, App. Num. Math. 13, 57-67 (1993).
4. T.E. Simos, A new variable-step method for the numerical integration of second-order IVP and their application to one-dimensional Schrödinger equation, Appl. Math. Lett. 6 (3), 67-73 (1993).
5. P. Deuflhard, A study of extrapolation methods based on multistep schemes without parasitic solutions, ZAMP 30, 177-189 (1979).
6. E. Stiefel and D.G. Bettis, Stabilization of Cowell's method, Numer. Math. 13, 154-175 (1969).
7. G. Scheifele, On the numerical integration of perturbed linear oscillating systems, ZAMP 22, 186-210 (1971).
8. P. Martín and J.M. Ferrándiz, Multistep numerical methods based on Scheifele G-functions with application to satellite dynamics, SIAM J. Numer. Anal. 34, 359-375 (1997).
9. J. Vigo-Aguiar and J.M. Ferrándiz, High-order variable step algorithms adapted to the integration of perturbed oscillators, Computer Physics Communications (submitted).
10. L.M. Milne-Thomson, The Calculus of Finite Differences, The Macmillan Press, New York, (1981).
11. J. Vigo-Aguiar, An approach to variable coefficient multistep methods for special differential equations, Discussion Paper VA197, Dept. Matemática Aplicada, Univ. Alicante, (1996).
12. J.D. Lambert, Numerical Methods for Ordinary Differential Systems, John Wiley and Sons, New York, (1991).
13. H.J. Stetter, Analysis of Discretization Methods for Ordinary Differential Equations, Springer, Berlin, (1973).
14. R.D. Grigorieff, Stability of multistep methods on variable grids, Numer. Math. 42, 359-377 (1983).