TY - JOUR
A2 - Liou, Yeong-Cheng
AU - Shi, Chunmei
AU - Xiao, Yu
AU - Zhang, Chiping
PY - 2012
DA - 2012/09/04
TI - The Convergence and MS Stability of Exponential Euler Method for Semilinear Stochastic Differential Equations
SP - 350407
VL - 2012
AB - The numerical approximation of exponential Euler method is constructed for semilinear stochastic differential equations (SDEs). The convergence and mean-square(MS) stability of exponential Euler method are investigated. It is proved that the exponential Euler method is convergent with the strong order 1/2 for semilinear SDEs. A mean-square linear stability analysis shows that the stability region of exponential Euler method contains that of EM method and stochastic Theta method (0≤θ<1) and also contains that of the scale linear SDE, that is, exponential Euler method is analogue mean-square A-stable. Then the exponential stability of the exponential Euler method for scalar semi-linear SDEs is considered. Under the conditions that guarantee the analytic solution is exponentially stable in mean-square sense, the exponential Euler method can reproduce the mean-square exponential stability for any nonzero stepsize. Numerical experiments are given to verify the conclusions.
SN - 1085-3375
UR - https://doi.org/10.1155/2012/350407
DO - 10.1155/2012/350407
JF - Abstract and Applied Analysis
PB - Hindawi Publishing Corporation
KW -
ER -