Positive results are proved here about the ability of balanced methods to reproduce the mean square stability of the impulsive stochastic differential equations. It is shown that the balanced methods with strong convergence can preserve the mean square stability with the sufficiently small stepsize. Weak variants and their mean square stability are also considered. Several numerical experiments are given for illustration and show that the fully implicit methods are superior to those of the explicit methods in terms of mean-square stabilities for relatively large stepsizes especially.
This article is a survey on the progress in the study of the generalized Riemann problems for MD Euler system. A new result on generalized Riemann problems for Euler systems containing all three main nonlinear waves(shock, rarefaction wave and contact discontinuity) is also introduced.
