IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v541y2020ics0378437119318515.html
   My bibliography  Save this article

Numerical simulations for stochastic differential equations on manifolds by stochastic symmetric projection method

Author

Listed:
  • Wang, Zhenyu
  • Wang, Chenke
  • Ma, Qiang
  • Ding, Xiaohua

Abstract

Stochastic standard projection technique, as an efficient approach to simulate stochastic differential equations on manifolds, is widely used in practical applications. However, stochastic standard projection methods usually destroy the geometric properties (such as symplecticity or reversibility), even though the underlying methods are symplectic or symmetric, which seriously affect long-time behavior of the numerical solutions. In this paper, a modification of stochastic standard projection methods for stochastic differential equations on manifolds is presented. The modified methods, called the stochastic symmetric projection methods, remain the symmetry and the ρ-reversibility of the underlying methods and maintain the numerical solutions on the correct manifolds. The mean square convergence order of these methods are proved to be the same as the underlying methods’. Numerical experiments are implemented to verify the theoretical results and show the superiority of the stochastic symmetric projection methods over the stochastic standard projection methods.

Suggested Citation

  • Wang, Zhenyu & Wang, Chenke & Ma, Qiang & Ding, Xiaohua, 2020. "Numerical simulations for stochastic differential equations on manifolds by stochastic symmetric projection method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    • Handle: RePEc:eee:phsmap:v:541:y:2020:i:c:s0378437119318515
    DOI: 10.1016/j.physa.2019.123305
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437119318515
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2019.123305?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Duan, Wei-Long & Fang, Hui & Zeng, Chunhua, 2019. "Second-order algorithm for simulating stochastic differential equations with white noises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 491-497.
    2. Tetsuya Misawa, 1999. "Conserved Quantities and Symmetries Related to Stochastic Dynamical Systems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 51(4), pages 779-802, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Duan, Wei-Long & Fang, Hui & Zeng, Chunhua, 2019. "The stability analysis of tumor-immune responses to chemotherapy system with gaussian white noises," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 96-102.
    2. Duan, Wei-Long & Lin, Ling, 2021. "Noise and delay enhanced stability in tumor-immune responses to chemotherapy system," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    3. Duan, Wei-Long & Fang, Hui, 2020. "The unified colored noise approximation of multidimensional stochastic dynamic system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    4. Francesco C. De Vecchi & Elisa Mastrogiacomo & Mattia Turra & Stefania Ugolini, 2021. "Noether Theorem in Stochastic Optimal Control Problems via Contact Symmetries," Mathematics, MDPI, vol. 9(9), pages 1-34, April.
    5. Francesco C. De Vecchi & Elisa Mastrogiacomo & Mattia Turra & Stefania Ugolini, 2021. "Noether theorem in stochastic optimal control problems via contact symmetries," Papers 2102.03172, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:541:y:2020:i:c:s0378437119318515. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.