Random generation of stochastic area integrals
SIAM Journal on Applied Mathematics
Stability Analysis of Numerical Schemes for Stochastic Differential Equations
SIAM Journal on Numerical Analysis
Variable step size control in the numerical solution of stochastic differential equations
SIAM Journal on Applied Mathematics
The composite Euler method for stiff stochastic differential equations
Journal of Computational and Applied Mathematics
Mean-Square and Asymptotic Stability of the Stochastic Theta Method
SIAM Journal on Numerical Analysis
Splitting for Dissipative Particle Dynamics
SIAM Journal on Scientific Computing
Numerical methods for nonlinear stochastic differential equations with jumps
Numerische Mathematik
SDELab: A package for solving stochastic differential equations in MATLAB
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Applied Numerical Mathematics
SIAM Journal on Numerical Analysis
Mathematics and Computers in Simulation
Stochastic Runge-Kutta Methods for Itô SODEs with Small Noise
SIAM Journal on Scientific Computing
Computers & Mathematics with Applications
Strong first order S-ROCK methods for stochastic differential equations
Journal of Computational and Applied Mathematics
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We are concerned with a linear mean-square stability analysis of numerical methods applied to systems of stochastic differential equations (SDEs) and, in particular, consider the @q-Maruyama and the @q-Milstein method in this context. We propose an approach, based on the vectorisation of matrices and the Kronecker product, that allows us to deal efficiently with the matrix expressions arising in this analysis and that provides the explicit structure of the stability matrices in the general case of linear systems of SDEs. For a set of simple test SDE systems, incorporating different noise structures but only a few parameters, we apply the general results and provide visual and numerical comparisons of the stability properties of the two methods.