Modification of the Richardson-Panovsky methods for precise integration of satellite orbits

Computers and Mathematics with Applications

Volumn 45, Issue 1-3, 2003, Pages 25-36

  Vigo Aguiar, J ^a   Richardson, D L ^b  

^a UNIVERSITY OF SALAMANCA   (Spain)

^b University of Cincinnati   (United States)

Author keywords

Chebyshev methods; Numerical integration

Indexed keywords

INTEGRATION; ITERATIVE METHODS; MATHEMATICAL TRANSFORMATIONS; ORBITS; PERTURBATION TECHNIQUES; RUNGE KUTTA METHODS; SATELLITES; SECOND HARMONIC GENERATION;

SATELLITE ORBITS;

INTERPOLATION;

EID: 0037286942     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0898-1221(03)80004-4     Document Type: Article

References (19)

1. J. Panovsky and D.L. Richardson, A family of implicit Chebyshev methods for the numerical integration of second-order ordinary differential equations, J. of Computational and Applied Mathematics 23, 35, (1988).
2. J.P. Coleman and A.S. Booth, Analysis of a family of Chebyshev methods for y″ = f(x, y), J. of Computational and Applied Mathematics 44, 95, (1992).
3. D.L. Richardson, A family of implicit Chebyshev methods for the numerical integration of first-order differential equations, AAS/AIAA Paper No. 93-691, (1993).
4. J. Vigo-Aguiar, Doctoral Dissertation (in Spanish), U. of Valladolid (1993).
5. C. Lanczos, Applied Analysis, Prentice-Hall, Englewood Cliffs, NJ, (1956).
6. C.W. Clenshaw, Numerical solution of ordinary differential equations in Chebyshev series, In P.L C.C. Symposium on Differential and Integral Equations, Rome, p. 222, Birkhäuser Verlag, (1960).
7. C.W. Clenshaw and H.J. Norton, The solution of nonlinear ordinary differential equations in Chebyshev series, Computer J. 6, 88, (1963).
8. H.J. Norton, The iterative solution of nonlinear ordinary differential equations in Chebyshev series, Computer J. 7, 76, (1964).
9. T. Lyche, Chebyshevian multistep methods for ordinary differential equations, Numer. Math. 19, 65, (1972).
10. E. Stiefel and D.G. Bettis, Stabilization of Cowell's method, Numer. Math. 13, 154, (1969).
11. L. Fox and I.B. Parker, Chebyshev Polynomials in Numerical Analysis, Oxford U. Press, London, (1968).
12. M. Snyder, Chebyshev Methods in Numerical Approximation, Prentice-Hall, Englewood Cliffs, NJ, (1966).
13. J. Panovsky and D.L. Richardson, A method for the numerical integration of ordinary differential equations using Chebyshev polynomials, AAS/AIAA Paper No. 85-405, (1985).
14. C.W. Clenshaw, Chebyshev series for mathematical functions, In Mathematical Tables, Vol. 5, Her Majesty's Stationery Office, London, (1962).
15. P. Henrici, Discrete Variable Methods in Ordinary Differential Equations, John Wiley, New York, (1962).
16. E.L. Stiefel and G. Scheifele, Linear and Regular Celestial Mechanics, Springer-Verlag, New York, (1971).
17. W.H. Press, S.A. Teukolsky and W.T. Vetterling, Numerical Recipes in Fortran. The Art of Scientific Computing, Cambridge University Press, Cambridge, (1992).
18. R. Bulirseh and J. Stoer, Numerical treatment of ordinary differential equations by extrapolation methods, Numer. Math. 8, 1, (1966).
19. J. Vigo-Aguiar and J.M. Ferrándiz, A general procedure to construct adapted multistep methods to oscillatory problems, SIAM J. of Num. Anal. 38, 1684-1708, (1998).