Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
An introduction to difference equations
An introduction to difference equations
Stability Analysis of Numerical Schemes for Stochastic Differential Equations
SIAM Journal on Numerical Analysis
Scientific Computing with Ordinary Differential Equations
Scientific Computing with Ordinary Differential Equations
Mean-Square and Asymptotic Stability of the Stochastic Theta Method
SIAM Journal on Numerical Analysis
Multistep methods for SDEs and their application to problems with small noise
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Mathematics and Computers in Simulation
Mean-square stability analysis of numerical schemes for stochastic differential systems
Journal of Computational and Applied Mathematics
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The mean-square stability for two-step schemes applied to scalar stochastic differential equations is studied. Necessary and sufficient conditions in terms of the parameters of the schemes guaranteeing their MS-stability are derived. Particular members of the studied family are considered, their stability regions are plotted and compared with the stability region of the linear test equation. It is proved that the stochastic two-step BDF scheme is unconditionally MS-stable. Numerical experiments that confirm the theoretical results are shown.