Stability Analysis of Numerical Schemes for Stochastic Differential Equations
SIAM Journal on Numerical Analysis
Strong discrete time approximation of stochastic differential equations with time delay
Mathematics and Computers in Simulation
Numerical solutions of stochastic differential equations — implementation and stability issues
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Mean-Square and Asymptotic Stability of the Stochastic Theta Method
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Delay-dependent stability of high order Runge–Kutta methods
Numerische Mathematik
Journal of Computational and Applied Mathematics
International Journal of Computer Mathematics
Journal of Computational and Applied Mathematics
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This paper is concerned with the numerical solution of stochastic delay differential equations. The focus is on the delay-dependent stability of numerical methods for a linear scalar test equation with real coefficients. By using the so-called root locus technique, the full asymptotic stability region in mean square of stochastic theta methods is obtained, which is characterized by a sufficient and necessary condition in terms of the drift and diffusion coefficients as well as time stepsize and method parameter theta. Then, this condition is compared with the analytical stability condition. It is proved that the Backward Euler method completely preserves the asymptotic mean square stability of the underlying system and the Euler-Maruyama method preserves the instability of the system. Our investigation also shows that not all theta methods with @q=12 preserve this delay-dependent stability. Some numerical examples are presented to confirm the theoretical results.