非线性随机延迟微分方程半隐式Euler方法的收敛性

 首先利用附近已有节点上的值通过插值对延迟项进行数值逼近,然后针对较一般情形下的一类非线性随机延迟微分方程初值问题,得到了带线性插值的半隐式Euler方法在均方意义下是收敛的理论结果,它推广了已有文献中的相关结论.

Convergence of semi-implicit Euler methods for nonlinear stochastic delay differential equations

It is concerned with the error analysis of semi-implicit Euler methods applied to a general class of nonlinear stochastic delay differential equations. A new attempt to get the numerical approximation of the delay argument is presented,i, e, the delay argument is solved by interpolating. It is proved that the semi-implicit Euler methods with linear interpolation procedure is convergent. Moreover, the results can be regarded as a extension of the similar conclusions in the present documents.