On a method for numerical integration of differential equations

Details On a method for numerical integration of differential equations On a method for numerical integration of differential equations

Mar 1976

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1976kosis..14..300b&link_type=abstract

Kosmicheskie Issledovaniia, vol. 14, Mar.-Apr. 1976, p. 300, 301. In Russian.

Mathematics

Differential Equations, Numerical Integration, Orbit Calculation, Satellite Orbits, Harmonic Analysis, Legendre Functions, Orbit Perturbation, Runge-Kutta Method, Series (Mathematics)

Scientific paper

A system of equations in osculating elements is presented to illustrate a method of speeding up numerical integration of differential equations. A new independent variable, the unperturbed argument of the satellite latitude, is entered, eliminating the rapidly varying time from the system of equations. The time can be determined directly from Kepler's equations without iterations. The effect of the second harmonic in the Legendre polynomial series expansion of the geopotential can be used as a perturbation. A constant integration step in the transformation corresponds to a variable step in integration over time. Runge-Kutta computations with automatically selected integration steps can be compressed considerably by this method.

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