# 2–stage stochastic Runge–Kutta for stochastic delay differential equations

## Abstract

This paper proposes a newly developed one-step derivative-free method, that is 2-stage stochastic Runge-Kutta (SRK2) to approximate the solution of stochastic delay differential equations (SDDEs) with a constant time lag, r > 0. General formulation of stochastic Runge-Kutta for SDDEs is introduced and Stratonovich Taylor series expansion for numerical solution of SRK2 is presented. Local truncation error of SRK2 is measured by comparing the Stratonovich Taylor expansion of the exact solution with the computed solution. Numerical experiment is performed to assure the validity of the method in simulating the strong solution of SDDEs.

- Authors:

- Faculty of Industrial Science and Technology, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300, Gambang, Pahang (Malaysia)
- Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 Johor Bahru, Johor (Malaysia)

- Publication Date:

- OSTI Identifier:
- 22391649

- Resource Type:
- Journal Article

- Journal Name:
- AIP Conference Proceedings

- Additional Journal Information:
- Journal Volume: 1660; Journal Issue: 1; Conference: ICoMEIA 2014: International Conference on Mathematics, Engineering and Industrial Applications 2014, Penang (Malaysia), 28-30 May 2014; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; COMPARATIVE EVALUATIONS; DIFFERENTIAL EQUATIONS; ERRORS; EXACT SOLUTIONS; RUNGE-KUTTA METHOD; SERIES EXPANSION; STOCHASTIC PROCESSES

### Citation Formats

```
Rosli, Norhayati, Jusoh Awang, Rahimah, Bahar, Arifah, and Yeak, S. H.
```*2–stage stochastic Runge–Kutta for stochastic delay differential equations*. United States: N. p., 2015.
Web. doi:10.1063/1.4915639.

```
Rosli, Norhayati, Jusoh Awang, Rahimah, Bahar, Arifah, & Yeak, S. H.
```*2–stage stochastic Runge–Kutta for stochastic delay differential equations*. United States. doi:10.1063/1.4915639.

```
Rosli, Norhayati, Jusoh Awang, Rahimah, Bahar, Arifah, and Yeak, S. H. Fri .
"2–stage stochastic Runge–Kutta for stochastic delay differential equations". United States. doi:10.1063/1.4915639.
```

```
@article{osti_22391649,
```

title = {2–stage stochastic Runge–Kutta for stochastic delay differential equations},

author = {Rosli, Norhayati and Jusoh Awang, Rahimah and Bahar, Arifah and Yeak, S. H.},

abstractNote = {This paper proposes a newly developed one-step derivative-free method, that is 2-stage stochastic Runge-Kutta (SRK2) to approximate the solution of stochastic delay differential equations (SDDEs) with a constant time lag, r > 0. General formulation of stochastic Runge-Kutta for SDDEs is introduced and Stratonovich Taylor series expansion for numerical solution of SRK2 is presented. Local truncation error of SRK2 is measured by comparing the Stratonovich Taylor expansion of the exact solution with the computed solution. Numerical experiment is performed to assure the validity of the method in simulating the strong solution of SDDEs.},

doi = {10.1063/1.4915639},

journal = {AIP Conference Proceedings},

issn = {0094-243X},

number = 1,

volume = 1660,

place = {United States},

year = {2015},

month = {5}

}

DOI: 10.1063/1.4915639

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