Numerical solution of stochastic state-dependent delay differential equations: convergence and stability
Abstract 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 t...
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2019-09-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2323-x |
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doaj-3b07efe950d04afaa1b5ef6f024a8bf92020-11-25T02:41:53ZengSpringerOpenAdvances in Difference Equations1687-18472019-09-012019113410.1186/s13662-019-2323-xNumerical solution of stochastic state-dependent delay differential equations: convergence and stabilityBahar Akhtari0Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS)Abstract 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.http://link.springer.com/article/10.1186/s13662-019-2323-x |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Bahar Akhtari |
| spellingShingle |
Bahar Akhtari Numerical solution of stochastic state-dependent delay differential equations: convergence and stability Advances in Difference Equations |
| author_facet |
Bahar Akhtari |
| author_sort |
Bahar Akhtari |
| title |
Numerical solution of stochastic state-dependent delay differential equations: convergence and stability |
| title_short |
Numerical solution of stochastic state-dependent delay differential equations: convergence and stability |
| title_full |
Numerical solution of stochastic state-dependent delay differential equations: convergence and stability |
| title_fullStr |
Numerical solution of stochastic state-dependent delay differential equations: convergence and stability |
| title_full_unstemmed |
Numerical solution of stochastic state-dependent delay differential equations: convergence and stability |
| title_sort |
numerical solution of stochastic state-dependent delay differential equations: convergence and stability |
| publisher |
SpringerOpen |
| series |
Advances in Difference Equations |
| issn |
1687-1847 |
| publishDate |
2019-09-01 |
| description |
Abstract 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. |
| url |
http://link.springer.com/article/10.1186/s13662-019-2323-x |
| work_keys_str_mv |
AT baharakhtari numericalsolutionofstochasticstatedependentdelaydifferentialequationsconvergenceandstability |
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1724776707024486400 |