Arbitrary order numerical methods conserving integrals for solving dynamic equations (Q1339317)

This paper is concerned with the numerical solution of some particular systems of ordinary differential equations conserving exactly a first integral or an invariant of the system. The numerical method proposed by the author is a modification of \textit{W. B. Gragg}'s extrapolation method [J. Soc. Ind. Appl. Math., Ser. 8, Numer. Anal. 2, 384-403 (1965; Zbl 0135.378)] with the coefficients of the linear combination of basic approximations chosen so that the integral under consideration is conserved. This approach is applied to some particular problems among them the \(N\)-bodies gravitational problem in a fixed inertial frame and in a rotating frame conserving the energy or Jacobi integral. Finally, since repeated extrapolation increases the order of the approximation in the standard Gragg method, the author proves a similar property for the modified extrapolation.