Analyzing Geometric Integrators

Abstract

In the previous chapter, we discussed the growth of error in numerical methods for differential equations. We saw that if the time interval is fixed, the error obeys the power law relationship with stepsize that is predicted by the convergence theory. We also saw that this did not contradict the exponential growth in the error with time (when the stepsize is fixed). The latter issue casts doubt on the reliance on the convergence order as a means for assessing the suitability of an integrator for molecular dynamics.