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://doi.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 - <p style="margin-top: 5px; text-align: justify;">We consider a midpoint scheme to approximate analytical solutions to a
white noise driven BBM equation that reads
du−du<sub>xx</sub>+u<sub>x</sub> ◦dW+u<sup>p</sup>u<sub>x</sub>dt=0.
We prove the well-posedness of the time-discrete approximation scheme and we provide the strong error order, which is 1.</p>