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Gauss-Jackson Method

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

y^('')=f(x,y)

first expounded by Gauss. It proceeds by introducing a function delta^(-2)f whose second differences are f. The advantage of this method is that summation to get delta^(-2) 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).

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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. and Crommelin, A. C. D. Investigation of the Motion of Halley's Comet from 1759 to 1910. Appendix to Greenwich Observations for 1909. Edinburgh, Scotland: H.M. Stationery Office, pp. 1-84, 1910.Jackson, J. "NOte on the Numerical Integration of d^2x/dt^2=f(x,t)." 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.

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Gauss-Jackson Method

Cite this as:

Weisstein, Eric W. "Gauss-Jackson Method." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Gauss-JacksonMethod.html

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