In this work, a novel second-order nonstandard finite difference (NSFD) method that preserves simultaneously the positivity and local asymptotic stability of one-dimensional autonomous dynamical systems is introduced analyzed. This based on non-local approximations for right-hand side functions differential equations in combination with denominator functions. The obtained results not only resol...

This paper is concerned with fully discrete mixed finite element approximations of the time-dependent stochastic Stokes equations multiplicative noise. A prototypical method, which comprises Euler–Maruyama scheme for time discretization and Taylor-Hood spatial studied in detail. Strong convergence rates established not only velocity approximation but also pressure (in a time-averaged fashion). ...

We give a nonstandard treatment of the notion of ends of proper geodesic metric spaces. We then apply this nonstandard treatment to Cayley graphs of finitely generated groups and give nonstandard proofs of many of the fundamental results concerning ends of groups. We end with an analogous nonstandard treatment of the ends of relatively Cayley graphs, that is Cayley graphs of cosets of finitely ...