Structure-preserving stochastic Runge–Kutta–Nyström methods for nonlinear second-order stochastic differential equations with multiplicative noise
Abstract A class of stochastic Runge–Kutta–Nyström (SRKN) methods for the strong approximation of second-order stochastic differential equations (SDEs) are proposed. The conditions for strong convergence global order 1.0 are given. The symplectic conditions for a given SRKN method to solve second-or...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-05-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | http://link.springer.com/article/10.1186/s13662-019-2133-1 |
| _version_ | 1818142996947795968 |
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| author | Qiang Ma Yuanwei Song Wei Xiao Wendi Qin Xiaohua Ding |
| author_facet | Qiang Ma Yuanwei Song Wei Xiao Wendi Qin Xiaohua Ding |
| author_sort | Qiang Ma |
| collection | DOAJ |
| description | Abstract A class of stochastic Runge–Kutta–Nyström (SRKN) methods for the strong approximation of second-order stochastic differential equations (SDEs) are proposed. The conditions for strong convergence global order 1.0 are given. The symplectic conditions for a given SRKN method to solve second-order stochastic Hamiltonian systems with multiplicative noise are derived. Meanwhile, this paper also proves that the stochastic symplectic Runge–Kutta–Nyström (SSRKN) methods conserve the quadratic invariants of underlying SDEs. Some low-stage SSRKN methods with strong global order 1.0 are obtained by using the order and symplectic conditions. Then the methods are applied to three numerical experiments to verify our theoretical analysis and show the efficiency of the SSRKN methods over long-time simulation. |
| first_indexed | 2024-12-11T11:24:39Z |
| format | Article |
| id | doaj.art-d8291380d5534332a30fa3f97d24329e |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-11T11:24:39Z |
| publishDate | 2019-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-d8291380d5534332a30fa3f97d24329e2022-12-22T01:09:03ZengSpringerOpenAdvances in Difference Equations1687-18472019-05-012019111810.1186/s13662-019-2133-1Structure-preserving stochastic Runge–Kutta–Nyström methods for nonlinear second-order stochastic differential equations with multiplicative noiseQiang Ma0Yuanwei Song1Wei Xiao2Wendi Qin3Xiaohua Ding4Department of Mathematics, Harbin Institute of Technology at WeihaiDepartment of Mathematics, Harbin Institute of Technology at WeihaiDepartment of Mathematics, Harbin Institute of Technology at WeihaiDepartment of Mathematics, Harbin Institute of Technology at WeihaiDepartment of Mathematics, Harbin Institute of Technology at WeihaiAbstract A class of stochastic Runge–Kutta–Nyström (SRKN) methods for the strong approximation of second-order stochastic differential equations (SDEs) are proposed. The conditions for strong convergence global order 1.0 are given. The symplectic conditions for a given SRKN method to solve second-order stochastic Hamiltonian systems with multiplicative noise are derived. Meanwhile, this paper also proves that the stochastic symplectic Runge–Kutta–Nyström (SSRKN) methods conserve the quadratic invariants of underlying SDEs. Some low-stage SSRKN methods with strong global order 1.0 are obtained by using the order and symplectic conditions. Then the methods are applied to three numerical experiments to verify our theoretical analysis and show the efficiency of the SSRKN methods over long-time simulation.http://link.springer.com/article/10.1186/s13662-019-2133-1Second-order stochastic differential equationsStochastic Hamiltonian systemsStochastic Runge–Kutta–Nyström methodsSymplectic integrators |
| spellingShingle | Qiang Ma Yuanwei Song Wei Xiao Wendi Qin Xiaohua Ding Structure-preserving stochastic Runge–Kutta–Nyström methods for nonlinear second-order stochastic differential equations with multiplicative noise Advances in Difference Equations Second-order stochastic differential equations Stochastic Hamiltonian systems Stochastic Runge–Kutta–Nyström methods Symplectic integrators |
| title | Structure-preserving stochastic Runge–Kutta–Nyström methods for nonlinear second-order stochastic differential equations with multiplicative noise |
| title_full | Structure-preserving stochastic Runge–Kutta–Nyström methods for nonlinear second-order stochastic differential equations with multiplicative noise |
| title_fullStr | Structure-preserving stochastic Runge–Kutta–Nyström methods for nonlinear second-order stochastic differential equations with multiplicative noise |
| title_full_unstemmed | Structure-preserving stochastic Runge–Kutta–Nyström methods for nonlinear second-order stochastic differential equations with multiplicative noise |
| title_short | Structure-preserving stochastic Runge–Kutta–Nyström methods for nonlinear second-order stochastic differential equations with multiplicative noise |
| title_sort | structure preserving stochastic runge kutta nystrom methods for nonlinear second order stochastic differential equations with multiplicative noise |
| topic | Second-order stochastic differential equations Stochastic Hamiltonian systems Stochastic Runge–Kutta–Nyström methods Symplectic integrators |
| url | http://link.springer.com/article/10.1186/s13662-019-2133-1 |
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