Numerical schemes for ordinary delay differential equations with random noise

Y. Asai and P.E. Kloeden

Applied Mathematics and Computation, 2019, vol. 347, issue C, 306-318

Abstract: Random ordinary differential equations (RODEs) are ordinary differential equations (ODEs) which have a stochastic process in their vector field functions. They have been used in a wide range of applications such as biology, medicine and engineering and play an important role in the theory of random dynamical systems. RODEs can be investigated pathwise as deterministic ODEs, however, the classical numerical methods for ODEs do not attain original order of convergence because the stochastic process has at most Hölder continuous sample paths and the resulting vector is also at most Hölder continuous in time. Recently, Jenzen & Kloeden derived new class of numerical methods for RODEs using integral versions of implicit Taylor-like expansions and developed arbitrary higher order schemes for RODEs. Their idea can be applied to random ordinary delay differential equations (RODDEs) by implementing Taylor-like expansions in the corresponding delay term. In this paper, numerical methods for RODDEs are systematically constructed based on Taylor-like expansions and they are applied to virus dynamics model with random fluctuations and time delay.

Keywords: Random ODE; Delay ODE; Pathwise convergence; Virus dynamics (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300318310075
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:347:y:2019:i:c:p:306-318

DOI: 10.1016/j.amc.2018.11.033

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().