## THERMAL SCIENCE

International Scientific Journal

### COMPACT SCHEMES FOR KORTEWEG-DE VRIES EQUATION

**ABSTRACT**

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.

**KEYWORDS**

PAPER SUBMITTED: 2016-06-13

PAPER REVISED: 2016-08-05

PAPER ACCEPTED: 2017-05-19

PUBLISHED ONLINE: 2017-09-09

**THERMAL SCIENCE** YEAR

**2017**, VOLUME

**21**, ISSUE

**Issue 4**, PAGES [1797 - 1806]

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