Mean-Square Stability of Euler Method For Nonlinear Neutral Stochastic Delay Differential Equations
Stochastic differential equations can always simulate the scientific problem in practical truthfully. They have been widely used in Physics, Chemistry, Cybernetics, Finance, Neural Networks, Bionomics, etc. So far there are not many results on the numerical stability of nonlinear neutral stochastic delay differential equations. The purpose of our work is to show that the Euler method applied to the nonlinear neutral stochastic delay differential equations is mean square stable under the condition which guarantees the stability of the analytical solution. The main aim of this paper is to establish new results on the numerical stability. It is proved that the Euler method is mean-square stable under suitable condition, i.e., assume the some conditions are satisfied, then, the Euler method applied to the nonlinear neutral stochastic delay differential equations with initial data is mean-square stable. Moreover, the theoretical result is also verified by a numerical example.
Neutral stochastic delay differential equations Euler method mean-square stable
Wenqiang Wang
School of Mathematics and Computational Science Xiangtan University Xiangtan, China
国际会议
武汉
英文
366-369
2011-08-20（万方平台首次上网日期，不代表论文的发表时间）