Error analysis can tell you whether the roundoff error would grow exponentially with time steps for the algorithm you use. If you avoid this kind of conditions

Error analysis can tell you whether the roundoff error would grow exponentially with time steps for the algorithm you use. If you avoid this kind of conditions in scientific computing, then double precision floating point number would work perfectly fine. And by the way, scientific computing is a diverse discipline, or a federation of disciplines. Say, there may be little overlap between the algorithms, tools, and environments that a physicist uses for scientific computing and those used by a bioinformatician. So I don't think it is universally true in scientific computing that arbitrary precision is preferable to double precision.