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A discussion of time transformations and local truncation errors

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Abstract

A review and discussion of several investigations concerning the effect of time transformations on numerical integration errors is given. In particular, the discussion treats the relation between time transformations andlocal truncation errors.

Additional numerical results are presented which indicate that time transformations reducelocal truncation errors. The results complement those of other studies, especially the recent studies of Danby, Wong, Velez, and Feagin and Mikkilineni. A Sundman time transformation with avarying exponent is introduced and discussed.

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References

  • Baumgarte, J.: 1972,Celestial Mechanics, Vol. 2, p. 281.

    Google Scholar 

  • Bettis, D. and Szebehely, V.: 1971,Astrophysics and Space Science, Vol. 14, No. 1, p. 133.

    Google Scholar 

  • Buechler, G. and Walker, D. C.: 1970, Report No. TOR-0066 (9320)-2, Vol. III, The Aerospace Corp., El Sequndo, California.

  • Burdet, C. A.: 1969,Journal fur die reine und angewandte Mathematik, Band 238, Seite 71, bis 84.

  • Czuchry, A. J. and Pitkin, E. T.: 1970,Journal of Spacecraft and Rockets, Vol. 7, No. 7, p. 882.

    Google Scholar 

  • Danby, J. M. A.: 1972,Celestial Mechanics, Vol. 5, No. 3, p. 311.

    Google Scholar 

  • Feagin, T. and Mikkilineni, R. P.: 1976, this issue, p. 491.

  • Janin, G.: 1974,Celestial Mechanics, Vol. 10, No. 4, p. 451.

    Google Scholar 

  • Nacozy, P.: 1971,Astrophysics and Space Science, Vol. 14, No. 1, p. 40.

    Google Scholar 

  • Nacozy, P.: 1972,American Institute of Aeronautics and Astronautics Journal, Vol. 10, No. 5, p. 704.

    Google Scholar 

  • Nacozy, P.: 1973,Bulletin of the American Astronomical Society, Vol. 5, No. 1, p. 421.

    Google Scholar 

  • Nacozy, P.: 1974, “Time Elements,” appears inSatellite Dynamics, ed. by G. Giacaglia, Springer-Verlag Pub.

  • Stiefel, E. 1970,Celestial Mechanics, Vol. 2, No. 3, p. 274.

    Google Scholar 

  • Stiefel, E. and Scheifele, G. 1971,Linear and Regular Celestial Mechanics, Springer-Verlag, Berlin.

    Google Scholar 

  • Sundman, K. F. 1912,Acta Mathematik, Vol. 36, p. 105.

    Google Scholar 

  • Szebehely, V. and Pierce, D. A. 1967,American Institute of Aeronautics and Astronautics, Vol. 5, No. 8, p. 1520.

    Google Scholar 

  • Tapley, B. D., Szebehely, V. and Lewallen, J. M. 1969,American Institute of Aeronautics and Astronautics, Vol. 7, No. 5, p. 1010.

    Google Scholar 

  • Velez, C. E. 1974,Celestial Mechanics, Vol. 10, No. 4, p. 405.

    Google Scholar 

  • Velez, C. E.: 1976, Proceedings of the NATO Advanced Study Institute on Long-time Predictions in Dynamics, ed. by B. Tapley and V. Szebehely, D. Reidel Publ. (in print).

  • Wong, P.: 1972,Some Special Perturbation Methods for the Integration of Artificial Satellite Orbits, UCLA Doctoral Dissertation (available from University Microfilms, Ann Arbor, Michigan, No. 72-20, 485).

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  1. University of Texas at Austin, Austin, USA

    Paul Nacozy

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  1. Paul Nacozy
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Nacozy, P. A discussion of time transformations and local truncation errors. Celestial Mechanics 13, 495–501 (1976). https://doi.org/10.1007/BF01229102

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  • DOI: https://doi.org/10.1007/BF01229102

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