Modelling uncertainties in the stationary seepage problem
This paper considers the uncertainties in the stationary seepage problem. Initially, this investigation considers the uncertainties in the results of a finite element method analysis of a stationary seepage problem, where the properties of the porous medium can be considered as random variables. Random field theory is introduced to describe the uncertainty in the hydraulic properties of a porous media. The method of updating of stochastic random fields, under the condition that some of their sample realisations are observed and known is outlined. 1 Introduction In the modelling of seepage problems in porous media many kinds of simplifications are used which can introduce uncertainty into the results of the analysis, as illustrated by the following examples; (i) hydraulic characteristics can be considered a
The paper deals with the stability of the semi-implicit Milstein method for stochastic differential e-quations with time delay. By studying the difference equation, which is the outcome of applying the numerical method to a linear test equation, conditions under which the method is MS-stable and GMS-stable are determined. Moreover, some numerical experiments are given.