A small time solutions for the Korteweg-de Vries equation using spline approximation

In this paper the one-dimensional nonlinear Korteweg-de Vries (KdV) equation is numerically solved using second order spline approximation. The test problems concerning the propagation of a solution and two solution interaction are used to validate the proposal scheme and it is found to be both accurate and efficient at small times. Also, it is shown that the second order spline approximation may be used effectively at small times when the exact solution of the KdV equation is not known.