TY - JOUR
TI - Compact schemes for Korteweg-de Vries equation
AU - Yin Xiu-Ling
AU - Zhang Cheng-Jian
AU - Zhang Jing-Jing
AU - Liu Yan-Qin
JN - Thermal Science
PY - 2017
VL - 21
IS - 4
SP - 1797
EP - 1806
PT - Article
AB - This paper proposes one family of compact schemes for Korteweg-de Vries equation. In the deterministic case, the schemes are convergent with fourth-order accuracy both in space and in time. Moreover, the schemes are stable. The numerical dispersion relation is analyzed. We compare the schemes with one second-order scheme. The numerical examples test the effect of the schemes. In the stochastic case, we simulate the wave profile and three discrete dynamical quantities for Korteweg-de Vries equation with small noise. The white noise has stochastic influence on the profile and dynamical quantities of the solution. If the size of noise increases, the perturbation on the profile and dynamical quantities will increase accordingly.