On some estimations of deviations between real solution and numerical solution of dynamical equations with regard for Baumgarte constraint stabilization

Abstract

The numerical solution of a system of differential equations with constraints can be unstable due to the accumulation of rounding errors during the implementation of the difference scheme of numerical integration. To limit the amount of accumulation, the Baumgarte constraint stabilization method is used. In order to estimate the deviation of real solution from the numerical one the method of constraint stabilization can be used to derive required formulas. The well-known technique of expansion the deviation function to Taylor series is being used. The paper considers the estimation of the error of the numerical solution obtained by the first-order Euler method.