An Application of Modified Equation to Reduce Some Numerical Instabilities

The presence of errors in the initial conditions and the different physical parameters affect to numerical integration of equations of motion necessarily. It is interesting to determine which the causes of the possible phase errors are and/or the dumping/dissipative terms that can appear. The modified equation can be useful to reduce numerical instability errors which may be confused by geometrical or physical errors. This is a necessary first step to detect another kind of errors related to the mathematical/physical model and not to the integration method.