Performance of Eular-Maruyama, 2-stage SRK and 4-stage SRK in approximating the strong solution of stochastic model

Stochastic differential equations play a prominent role in many application areas including finance, biology and epidemiology. By incorporating random elements to ordinary differential equation system, a system of stochastic differential equations (SDEs) arises. This leads to a more complex insight...

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Main Authors:	Norhayati Rosli, Arifah Bahar, Yeak, Su Hoe, Haliza Abdul Rahman, Madihah Md. Salleh
Format:	Article
Language:	English
Published:	Universiti Kebangsaan Malaysia 2010
Online Access:	http://journalarticle.ukm.my/7416/ http://journalarticle.ukm.my/7416/ http://journalarticle.ukm.my/7416/1/01_Md_Yeaminhossain.pdf

id	ukm-7416
recordtype	eprints
spelling	ukm-74162016-12-14T06:44:01Z http://journalarticle.ukm.my/7416/ Performance of Eular-Maruyama, 2-stage SRK and 4-stage SRK in approximating the strong solution of stochastic model Norhayati Rosli, Arifah Bahar, Yeak, Su Hoe Haliza Abdul Rahman, Madihah Md. Salleh, Stochastic differential equations play a prominent role in many application areas including finance, biology and epidemiology. By incorporating random elements to ordinary differential equation system, a system of stochastic differential equations (SDEs) arises. This leads to a more complex insight of the physical phenomena than their deterministic counterpart. However, most of the SDEs do not have an analytical solution where numerical method is the best way to resolve this problem. Recently, much work had been done in applying numerical methods for solving SDEs. A very general class of Stochastic Runge-Kutta, (SRK) had been studied and 2-stage SRK with order convergence of 1.0 and 4-stage SRK with order convergence of 1.5 were discussed. In this study, we compared the performance of Euler-Maruyama, 2-stage SRK and 4-stage SRK in approximating the strong solutions of stochastic logistic model which describe the cell growth of C. acetobutylicum P262. The MS-stability functions of these schemes were calculated and regions of MS-stability are given. We also perform the comparison for the performance of these methods based on their global errors. Universiti Kebangsaan Malaysia 2010-10 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/7416/1/01_Md_Yeaminhossain.pdf Norhayati Rosli, and Arifah Bahar, and Yeak, Su Hoe and Haliza Abdul Rahman, and Madihah Md. Salleh, (2010) Performance of Eular-Maruyama, 2-stage SRK and 4-stage SRK in approximating the strong solution of stochastic model. Sains Malaysiana, 39 (5). pp. 851-857. ISSN 0126-6039 http://www.ukm.my/jsm/english_journals/vol39num5_2010/contentsVol39num5_2010.html
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Kebangasaan Malaysia
building	UKM Institutional Repository
collection	Online Access
language	English
description	Stochastic differential equations play a prominent role in many application areas including finance, biology and epidemiology. By incorporating random elements to ordinary differential equation system, a system of stochastic differential equations (SDEs) arises. This leads to a more complex insight of the physical phenomena than their deterministic counterpart. However, most of the SDEs do not have an analytical solution where numerical method is the best way to resolve this problem. Recently, much work had been done in applying numerical methods for solving SDEs. A very general class of Stochastic Runge-Kutta, (SRK) had been studied and 2-stage SRK with order convergence of 1.0 and 4-stage SRK with order convergence of 1.5 were discussed. In this study, we compared the performance of Euler-Maruyama, 2-stage SRK and 4-stage SRK in approximating the strong solutions of stochastic logistic model which describe the cell growth of C. acetobutylicum P262. The MS-stability functions of these schemes were calculated and regions of MS-stability are given. We also perform the comparison for the performance of these methods based on their global errors.
format	Article
author	Norhayati Rosli, Arifah Bahar, Yeak, Su Hoe Haliza Abdul Rahman, Madihah Md. Salleh,
spellingShingle	Norhayati Rosli, Arifah Bahar, Yeak, Su Hoe Haliza Abdul Rahman, Madihah Md. Salleh, Performance of Eular-Maruyama, 2-stage SRK and 4-stage SRK in approximating the strong solution of stochastic model
author_facet	Norhayati Rosli, Arifah Bahar, Yeak, Su Hoe Haliza Abdul Rahman, Madihah Md. Salleh,
author_sort	Norhayati Rosli,
title	Performance of Eular-Maruyama, 2-stage SRK and 4-stage SRK in approximating the strong solution of stochastic model
title_short	Performance of Eular-Maruyama, 2-stage SRK and 4-stage SRK in approximating the strong solution of stochastic model
title_full	Performance of Eular-Maruyama, 2-stage SRK and 4-stage SRK in approximating the strong solution of stochastic model
title_fullStr	Performance of Eular-Maruyama, 2-stage SRK and 4-stage SRK in approximating the strong solution of stochastic model
title_full_unstemmed	Performance of Eular-Maruyama, 2-stage SRK and 4-stage SRK in approximating the strong solution of stochastic model
title_sort	performance of eular-maruyama, 2-stage srk and 4-stage srk in approximating the strong solution of stochastic model
publisher	Universiti Kebangsaan Malaysia
publishDate	2010
url	http://journalarticle.ukm.my/7416/ http://journalarticle.ukm.my/7416/ http://journalarticle.ukm.my/7416/1/01_Md_Yeaminhossain.pdf
first_indexed	2023-09-18T19:49:38Z
last_indexed	2023-09-18T19:49:38Z
_version_	1777406132214562816

Performance of Eular-Maruyama, 2-stage SRK and 4-stage SRK in approximating the strong solution of stochastic model

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