Simulating Stochastic Differential Equations with Conserved Quantities by Improved Explicit Stochastic Runge–Kutta Methods
Explicit numerical methods have a great advantage in computational cost, but they usually fail to preserve the conserved quantity of original stochastic differential equations (SDEs). In order to overcome this problem, two improved versions of explicit stochastic Runge–Kutta methods are given such t...
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| Format: | Article |
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MDPI AG
2020-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/12/2195 |
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| author | Zhenyu Wang Qiang Ma Xiaohua Ding |
| author_facet | Zhenyu Wang Qiang Ma Xiaohua Ding |
| author_sort | Zhenyu Wang |
| collection | DOAJ |
| description | Explicit numerical methods have a great advantage in computational cost, but they usually fail to preserve the conserved quantity of original stochastic differential equations (SDEs). In order to overcome this problem, two improved versions of explicit stochastic Runge–Kutta methods are given such that the improved methods can preserve conserved quantity of the original SDEs in Stratonovich sense. In addition, in order to deal with SDEs with multiple conserved quantities, a strategy is represented so that the improved methods can preserve multiple conserved quantities. The mean-square convergence and ability to preserve conserved quantity of the proposed methods are proved. Numerical experiments are implemented to support the theoretical results. |
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| format | Article |
| id | doaj.art-9e2149e93cb94c46b0dd73b43b1bc833 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T14:11:55Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-9e2149e93cb94c46b0dd73b43b1bc8332023-11-21T00:05:16ZengMDPI AGMathematics2227-73902020-12-01812219510.3390/math8122195Simulating Stochastic Differential Equations with Conserved Quantities by Improved Explicit Stochastic Runge–Kutta MethodsZhenyu Wang0Qiang Ma1Xiaohua Ding2Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, ChinaDepartment of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, ChinaDepartment of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, ChinaExplicit numerical methods have a great advantage in computational cost, but they usually fail to preserve the conserved quantity of original stochastic differential equations (SDEs). In order to overcome this problem, two improved versions of explicit stochastic Runge–Kutta methods are given such that the improved methods can preserve conserved quantity of the original SDEs in Stratonovich sense. In addition, in order to deal with SDEs with multiple conserved quantities, a strategy is represented so that the improved methods can preserve multiple conserved quantities. The mean-square convergence and ability to preserve conserved quantity of the proposed methods are proved. Numerical experiments are implemented to support the theoretical results.https://www.mdpi.com/2227-7390/8/12/2195stochastic differential equationsexplicit stochastic Runge–Kutta methodsmean-square convergenceconserved quantities |
| spellingShingle | Zhenyu Wang Qiang Ma Xiaohua Ding Simulating Stochastic Differential Equations with Conserved Quantities by Improved Explicit Stochastic Runge–Kutta Methods Mathematics stochastic differential equations explicit stochastic Runge–Kutta methods mean-square convergence conserved quantities |
| title | Simulating Stochastic Differential Equations with Conserved Quantities by Improved Explicit Stochastic Runge–Kutta Methods |
| title_full | Simulating Stochastic Differential Equations with Conserved Quantities by Improved Explicit Stochastic Runge–Kutta Methods |
| title_fullStr | Simulating Stochastic Differential Equations with Conserved Quantities by Improved Explicit Stochastic Runge–Kutta Methods |
| title_full_unstemmed | Simulating Stochastic Differential Equations with Conserved Quantities by Improved Explicit Stochastic Runge–Kutta Methods |
| title_short | Simulating Stochastic Differential Equations with Conserved Quantities by Improved Explicit Stochastic Runge–Kutta Methods |
| title_sort | simulating stochastic differential equations with conserved quantities by improved explicit stochastic runge kutta methods |
| topic | stochastic differential equations explicit stochastic Runge–Kutta methods mean-square convergence conserved quantities |
| url | https://www.mdpi.com/2227-7390/8/12/2195 |
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