ABOUT EVALUATIONS OF NUMERICAL METHODS EFFICIENCY OF INTEGRATION
OF DYNAMIC MODELS IN CELESTIAL MECHANICS PROBLEMS
Borunov V.P.
Institute for High-Performance Computer Systems RAS, Moscow
Problem about reception of quantitative valuations of
efficiency of methods of a type Runge-Kutta is considered:
Fehlberg ( 5-8 orders ), Everhart ( 7-19 orders ), Dormand-Prince
of 8 order and of a extrapolation method of the variable order
( Odex ). These methods are considered as software package on
Fortran-77 .
The quantitative characteristics of efficiency of
integration are formulated. As these characteristics are
accepted:
a processor time at given step-by-step accuracy;
an error of the decision ( should in this case
the exact solution of a model problem be known).
The reception of quantitative valuations of efficiency is
based on realization of numerical experiment on dynamic models of
some problems of the celestial mechanics.
As dynamic models considered following problems:
space limited elliptical problem of 9 bodies, describing
movement of the asteroid
in a gravity field of the Sun and 8 large planets;
flat star problem, describing movement 7 stars in one
plane.
Results of numerical experiments in a kind of the tables and
graphics are received, on the basis of which are determined an
dependences of the characteristics of time and accuracy for the
various orders of vectorized methods, applied to various classes
of ordinary differential equations. On the basis of the received
characteristics the analysis and comparison of efficiency of
methods of numerical integration of the various orders is
conducted.