Introduction to the contents of issue 52:3

Excerpt

BIT has emerged as one of the primary publication channels for stochastic differential equations, SDE, a fruitful way to study a system where dynamic and random influences have to be considered simultaneously. We are very proud that! In this issue, we have three papers on the numerical treatment of SDEs. In the first one, Jamie Alcock and Kevin Burrage treat a stiff SDE by the quasi implicit balanced method and show how the stability advantage of implicit methods can be brought over to the stochastic case. A method that is strongly stable of order 1.0 is developed and tested on an application, the Sagirow’s satellite problem. The second to last paper in this issue, written by Xiaojie Wang, Siqing Gan, and Desheng Wang, treats a related problem. It studies a family of fully implicit Milstein methods of strong stability order 1.0, and illustrate its behavior on two specially designed test problems. In another paper, P.A. Cioica, S. Dahlke, N. Döhring, S. Kinzel, F. Lindner, T. Raasch, K. Ritter, and R.L. Schilling develop a wavelet algorithm for a Poisson equation with a random right hand side. Convergence in a Besov space setting is established, and the regularity is illustrated in a numerical example. …