Computational uncertainty principle in nonlinear ordinary differential equations (I)

摘要

In a majority of cases of long-time numerical integration forintial-value problems, round- off error has received littleattention. Using twenty-nine numerical methods, the influence ofround-off erro on numerical solutions is generally studied through alarge number of numerical experiments. Here we find that there existsa strong dependence on machine precision (which is a new kind of de- Pendence different from the sensitive dependence on initialconditions), maximally effective computa- Tion time (MECT) andoptimal stepsize (OS) in solving nonlinear ordinary differentialequations (ODEs) in finite machine precision.