Volume 26, Issue 5
Numerical Analysis of the Midpoint Scheme for the Generalized Benjamin-Bona-Mahony Equation with White Noise Dispersion

Guillaume Fenger, Olivier Goubet & Youcef Mammeri

Commun. Comput. Phys., 26 (2019), pp. 1397-1414.

Published online: 2019-08

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  • Abstract

We consider a midpoint scheme to approximate analytical solutions to a white noise driven BBM equation that reads du−duxx+ux ◦dW+upuxdt=0. We prove the well-posedness of the time-discrete approximation scheme and we provide the strong error order, which is 1.

  • Keywords

Stochastic long wave equations, midpoint scheme, strong order of convergence.

  • AMS Subject Headings

35Q53, 65C30, 65N12, 65N15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

guillaume.fenger@u-picardie.fr (Guillaume Fenger)

olivier.goubet@u-picardie.fr (Olivier Goubet)

youcef.mammeri@u-picardie.fr (Youcef Mammeri)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-26-1397, author = {Fenger , Guillaume and Goubet , Olivier and Mammeri , Youcef }, title = {Numerical Analysis of the Midpoint Scheme for the Generalized Benjamin-Bona-Mahony Equation with White Noise Dispersion}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {5}, pages = {1397--1414}, abstract = {

We consider a midpoint scheme to approximate analytical solutions to a white noise driven BBM equation that reads du−duxx+ux ◦dW+upuxdt=0. We prove the well-posedness of the time-discrete approximation scheme and we provide the strong error order, which is 1.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2019.js60.02}, url = {http://global-sci.org/intro/article_detail/cicp/13269.html} }
TY - JOUR T1 - Numerical Analysis of the Midpoint Scheme for the Generalized Benjamin-Bona-Mahony Equation with White Noise Dispersion AU - Fenger , Guillaume AU - Goubet , Olivier AU - Mammeri , Youcef JO - Communications in Computational Physics VL - 5 SP - 1397 EP - 1414 PY - 2019 DA - 2019/08 SN - 26 DO - http://dor.org/10.4208/cicp.2019.js60.02 UR - https://global-sci.org/intro/article_detail/cicp/13269.html KW - Stochastic long wave equations, midpoint scheme, strong order of convergence. AB -

We consider a midpoint scheme to approximate analytical solutions to a white noise driven BBM equation that reads du−duxx+ux ◦dW+upuxdt=0. We prove the well-posedness of the time-discrete approximation scheme and we provide the strong error order, which is 1.

Guillaume Fenger, Olivier Goubet & Youcef Mammeri. (2019). Numerical Analysis of the Midpoint Scheme for the Generalized Benjamin-Bona-Mahony Equation with White Noise Dispersion. Communications in Computational Physics. 26 (5). 1397-1414. doi:10.4208/cicp.2019.js60.02
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