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Asymptotical mean-square stability of linear θ-methods for stochastic pantograph differential equations: variable stepsize and transformation approach
International Journal of Computer Mathematics ( IF 1.7 ) Pub Date : 2021-06-04 , DOI: 10.1080/00207160.2021.1932841
Xiaochen Yang 1 , Zhanwen Yang 1 , Yu Xiao 1
Affiliation  

The paper deals with the asymptotical mean-square stability of the linear θ-methods under variable stepsize and transformation approach for stochastic pantograph differential equations. A limiting equation for the analysis of numerical stability is introduced by Kronecker products. Under the condition which guarantee the stability of exact solutions, the optimal stability region of the linear θ-methods under variable stepsize is given by using the limiting equation, i.e. θ(12,1], which is the same to the deterministic problems. Moreover, the linear θ-methods under the transformation approach are also considered and the result of the stability is improved for θ=12. Finally, numerical examples are given to illustrate the asymptotical mean-square stability under variable stepsize and transformation approach.



中文翻译:

随机受电弓微分方程线性θ方法的渐近均方稳定性:可变步长和变换方法

本文研究了随机缩放微分方程在变步长和变换方法下线性θ方法的渐近均方稳定性。Kronecker 产品引入了数值稳定性分析的极限方程。在保证精确解稳定性的条件下,利用极限方程给出了变步长下线性θ法的最优稳定区域,即θ(12,1],这与确定性问题相同。此外,还考虑了变换方法下的线性θ方法,提高了结果的稳定性θ=12. 最后,给出数值例子说明了变步长和变换方法下的渐近均方稳定性。

更新日期:2021-06-04
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