TY - JOUR
ID - 6263
TI - Stability of two classes of improved backward Euler methods for stochastic delay differential equations of neutral type
JO - Computational Methods for Differential Equations
JA - CMDE
LA - en
SN - 2345-3982
AU - Farkhondeh Rouz, Omid
AU - Ahmadian, Davood
AD - Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran
Y1 - 2017
PY - 2017
VL - 5
IS - 3
SP - 201
EP - 213
KW - Neutral stochastic delay differential equations
KW - Exponential mean-square stability
KW - Split-step (theta
KW - lambda)-backward Euler method
KW - Lyapunov exponent
DO -
N2 - This paper examines stability analysis of two classes of improved backward Euler methods, namely split-step $(\theta, \lambda)$-backward Euler (SSBE) and semi-implicit $(\theta,\lambda)$-Euler (SIE) methods, for nonlinear neutral stochastic delay differential equations (NSDDEs). It is proved that the SSBE method with $\theta, \lambda\in(0,1]$ can recover the exponential mean-square stability with some restrictive conditions on stepsize $\delta$, drift and diffusion coefficients, but the SIE method can reproduce the exponential mean-square stability unconditionally. Moreover, for sufficiently small stepsize, we show that the decay rate as measured by the Lyapunov exponent can be reproduced arbitrarily accurately. Finally, numerical experiments are included to confirm the theorems.
UR - https://cmde.tabrizu.ac.ir/article_6263.html
L1 - https://cmde.tabrizu.ac.ir/article_6263_5ce76ae675ed3f591df2c191f12c3d50.pdf
ER -