The uncertainty in scientific computing has induced serious accidents and disasters. New proposals are presented toward an uncertainty inference or management in scientific numerical
computing. The first important point is to share the knowledge on uncertainty with other
researchers. Sharing known uncertainties contributes to the uncertainty management. In addition,
for specific problems, one can prepare multiple programs with different rounding methods and/or
with different precisions, and can compare the results among the programs generated for the
specific problems. If differences appear among the results, it suggests that the specific program
may have some uncertainty problems, and has a lack of the precision or a lack of the digit number.
This second method provides a simple and effective inference method of the uncertainty. Uncertainty
comes from various sources from physical and mathematical model errors, unknown input
data, numerical model errors, insuficient numerical precision,
oating point precision, programming
errors, data processing errors, visualization errors, etc., as well as human errors. Another
uncertainty comes from the discretization step size of Δt or Δx in numerical computations. The
discretization step size of Δt or Δx must be selected appropriately in numerical computations in
order to describe short waves or fast phenomena concerned to the target problems. This uncertainty would be also reduced by multiple program computations with the different size of Δt and
Δx to find out the appropriate step size under keeping numerical stabilities. These uncertainty
reduction mechanisms are proposed in this paper.
