王文强, 李寿佛, 黄山. 非线性随机延迟微分方程半隐式Euler方法的收敛性[J]. 云南大学学报(自然科学版), 2008, 30(1): 11-15,20.
引用本文: 王文强, 李寿佛, 黄山. 非线性随机延迟微分方程半隐式Euler方法的收敛性[J]. 云南大学学报(自然科学版), 2008, 30(1): 11-15,20.
WANG Wen-qiang, LI Shou-fu, HUANG Shan. Convergence of semi-implicit Euler methods for nonlinear stochastic delay differential equations[J]. Journal of Yunnan University: Natural Sciences Edition, 2008, 30(1): 11-15,20.
Citation: WANG Wen-qiang, LI Shou-fu, HUANG Shan. Convergence of semi-implicit Euler methods for nonlinear stochastic delay differential equations[J]. Journal of Yunnan University: Natural Sciences Edition, 2008, 30(1): 11-15,20.

非线性随机延迟微分方程半隐式Euler方法的收敛性

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

  • 摘要: 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.

     

    Abstract: 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.

     

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