The Research About Stability And Convergence Of Stochastic K Step BDF Method For Nonlinear Stochastic Delay Differential Equations System

Various kinds of linear multi-step methods are constructed to solve the stochastic delay differential equations(SDDE)by many scholars,their stability and convergence have been studied.but the delayed items of drift coefficient and diffusion coefficient,are uniform.However;in practice,their delayed items are different,and they are ar-bitrary positive constant.This problem has not been studied.Therefore,a new kind of nonlinear SDDE is considered in this paper.The delayed items of drift coefficient and diffusion coefficient are different in this new system.Usually present the delayed items by ?1,?2,?1,?2 can be arbitrary positive constant.In this paper,k-step BDF method for the ordinary differential equation is applied to this new kind of nonlinear SDDE,We construct stochastic k-step BDF method,and develop the fundamental numerical analysis concerning their mean-square stability,mean-square convergence.apply stochastic k-step BDF method to one-dimensional SDDE,we derive conditions guaranteeing their mean-square consistency and order of convergence.The first part is the introduction.This paper introduce the background of stochas-tie delay differential equations and the Overseas and Domestic:Research Status,the innovation of this paper and the main content,and the related symbols of this paper.The second part,this paper construct a new kind of stochastic k step BDF method for the kind of nonlinear SDDE,and provide the related definitions and conclusions of its mean-square stability,mean-square consistency,mean square convergence.In the third section,this paper prove that mean square stability and mean square convergence of the stochastic k step BDF method.The fourth part,this paper apply stochastic k-step BDF method to one-dimensional SDDE,we derive conditions guaranteeing their mean-square consistency and order of convergence.The fifth part,this paper construct stochastic 3 step BDF method and verify its mean-square stability and order of mean-square convergence by numerical experiments through Matlab software.