Volume 51, Issue 1
Spectral Element Methods for Stochastic Differential Equations with Additive Noise

Chao Zhang, Dongya Gu & Dongya Tao

J. Math. Study, 51 (2018), pp. 76-88.

Published online: 2018-04

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  • Abstract

In this paper, we propose numerical schemes for stochastic differential equations driven by white noise and colored noise, respectively. For this purpose, we first discretize the white noise and colored noise, and give their regularity estimates. Then we use spectral element methods to solve the corresponding stochastic differential equations numerically. The approximation errors are derived, and the numerical results demonstrate high accuracy of the proposed schemes.

  • Keywords

Stochastic differential equations spectral element methods high accuracy

  • AMS Subject Headings

65M70, 65L60, 41A10 ,60H35

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

chaozhang@jsnu.edu.cn (Chao Zhang)

gdyjy1@163.com (Dongya Gu)

dongyatao@jsnu.edu.cn (Dongya Tao)

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  • RIS
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@Article{JMS-51-76, author = {Zhang , Chao and Gu , Dongya and Tao , Dongya}, title = {Spectral Element Methods for Stochastic Differential Equations with Additive Noise}, journal = {Journal of Mathematical Study}, year = {2018}, volume = {51}, number = {1}, pages = {76--88}, abstract = {

In this paper, we propose numerical schemes for stochastic differential equations driven by white noise and colored noise, respectively. For this purpose, we first discretize the white noise and colored noise, and give their regularity estimates. Then we use spectral element methods to solve the corresponding stochastic differential equations numerically. The approximation errors are derived, and the numerical results demonstrate high accuracy of the proposed schemes.

}, issn = {2617-8702}, doi = {https://doi.org/10.4208/jms.v51n1.18.05}, url = {http://global-sci.org/intro/article_detail/jms/11316.html} }
TY - JOUR T1 - Spectral Element Methods for Stochastic Differential Equations with Additive Noise AU - Zhang , Chao AU - Gu , Dongya AU - Tao , Dongya JO - Journal of Mathematical Study VL - 1 SP - 76 EP - 88 PY - 2018 DA - 2018/04 SN - 51 DO - http://doi.org/10.4208/jms.v51n1.18.05 UR - https://global-sci.org/intro/article_detail/jms/11316.html KW - Stochastic differential equations KW - spectral element methods KW - high accuracy AB -

In this paper, we propose numerical schemes for stochastic differential equations driven by white noise and colored noise, respectively. For this purpose, we first discretize the white noise and colored noise, and give their regularity estimates. Then we use spectral element methods to solve the corresponding stochastic differential equations numerically. The approximation errors are derived, and the numerical results demonstrate high accuracy of the proposed schemes.

Chao Zhang, Dongya Gu & Dongya Tao. (2019). Spectral Element Methods for Stochastic Differential Equations with Additive Noise. Journal of Mathematical Study. 51 (1). 76-88. doi:10.4208/jms.v51n1.18.05
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