Exponential finite-difference method applied to Korteweg-de Vries equation for small times

The Korteweg-de Vries equation is numerically solved by using the exponential finite-difference technique. The accuracy of computed solutions is examined by comparison with other numerical and analytical solutions using two examples. The close results agreement between the current results and the exact solutions confirms that the proposed finite-difference procedure is an effective technique for the solution of the Korteweg-de Vries equation at the small times.