Computational uncertainty principle in nonlinear ordinary differential equations (I)

摘要

In a majority of cases of long-time numerical integration for intial-value problems, round- off error has received little attention. Using twenty-nine numerical methods, the influence of round-off erro on numerical solutions is generally studied through a large number of numerical experiments. Here we find that there exists a strong dependence on machine precision (which is a new kind of de- Pendence different from the sensitive dependence on initial conditions), maximally effective computa- Tion time (MECT) and optimal stepsize (OS) in solving nonlinear ordinary differential equations (ODEs) in finite machine precision.