GENERALIZED MULTISTEP METHODS AND APPLICATIONS TO SATELLITE ORBIT TRAJECTORY COMPUTATION
Abstract
Recent ideas in the theory of multistep methods of solving a differential equation of the first order are extended to methods of solving the special second order equation y(double prime) = f(x,y). A slight modification of the usual multistep method permits a significantly higher order approximation of the difference equation to the differential equation without loss of stability. The method of constructing the generalized difference equation is based on a quasi-Hermite polynomial approximation. An outline of this theory is given along with some related unsolved problems. This method permits the construction of new classes of stable difference equations with high order of accuracy for solving both a first order differential equation and the above special second order equation. Some of the new methods have been tested in experiments including the computation of an unperturbed satellite orbit trajectory. Machine time used and accuracy obtained are compared with a standard multistep method. Although further theoretical and experimental work remains to be done towards the analysis of accumulated round-off error and truncation error in the new methods, it is expected that they can eventually be incorporated into efficient algorithms for solving the general equations of motion of an earth satellite.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 28, 1966
- Accession Number
- AD0642232
Entities
People
- James Dyer
Organizations
- System Development Corporation