Gauss-Jackson Method

A method for numerical solution of a second-order ordinary differential equation

first expounded by Gauss. It proceeds by introducing a function  whose second differences are . The advantage of this method is that summation to get  can be done exactly and that each rounding-off error in the correction term arises only a single time (Jeffreys and Jeffreys 1988, p. 300).

REFERENCES:

Berry, M. M. and Healy, L. M. "Implementation of Gauss-Jackson Integration for Orbit Propagation." J. Astronaut. Sci. 52, 331-357, 2004.

Cowell, P. H. Appendix to Greenwich Observations. Bellevue: 1909.

Jackson, J. "NOte on the Numerical Integration of ." Monthly Not. Roy. Astron. Soc. 84, 602-606, 1924.

Jeffreys, H. and Jeffreys, B. S. "The Gauss-Jackson Method." §9.14 in Methods of Mathematical Physics, 3rd ed. Cambridge, England: Cambridge University Press, pp. 300-301, 1988.