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

Rosli, Norhayati and Bahar, Arifah and Su Hoe, Yeak and Abdul Rahman, Haliza and Md. Salleh, Madihah (2010) Performance of Euler-Maruyama, 2-Stage SRK and 4-Stage SRK in approximating the strong solution of stochastic model. Jurnal Sains Malaysiana, 39 (5). pp. 851-857. ISSN 0126-6039

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Abstract

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.

Item Type:Article
Uncontrolled Keywords:2-stage stochastic Runge-Kutta, 4-stage stochastic Runge-Kutta, Euler-Maruyama, stochastic differential equations
Subjects:Q Science > Q Science (General)
Divisions:Biosciences and Bioengineering (Formerly known)
ID Code:26007
Deposited By: Liza Porijo
Deposited On:22 Jun 2012 07:52
Last Modified:22 Jun 2012 07:52

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