Numerical solution of stochastic state-dependent delay differential equations: convergence and stability

被引:2
作者
Akhtari, Bahar [1 ]
机构
[1] IASBS, Dept Math, Zanjan, Iran
关键词
BACKWARD EULER METHOD; EXPONENTIAL STABILITY; SCHEMES; APPROXIMATION; EXISTENCE;
D O I
10.1186/s13662-019-2323-x
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Numerical analysis of stochastic delay differential equations has been widely developed but frequently for the cases where the delay term has a simple feature. In this paper, we aim to study a more general case of delay term which has not been much discussed so far. We mean the case where the delay term takes random values. For this purpose, a new continuous split-step scheme is introduced to approximate the solution and then convergence in the mean-square sense is investigated. Moreover, given a test equation, the mean-square asymptotic stability of the scheme is presented. Numerical examples are provided to further illustrate the obtained theoretical results.
引用
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页数:34
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