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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Universiti Kebangsaan Malaysia
2010
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my-ukm.journal.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 |
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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/7416/1/01_Md_Yeaminhossain.pdf http://journalarticle.ukm.my/7416/ http://www.ukm.my/jsm/english_journals/vol39num5_2010/contentsVol39num5_2010.html |
| _version_ |
1643737118388781056 |
| score |
13.250246 |