The Quintic spline for solving the Korteweg-de Vries equation

The Korteweg-de Vries equation is numerically solved by using a new algorithm based on the quintic spline approximation. An iterative scheme having O(k2 + kh2) accuracy and five-band constant coefficients system of equations is devised. The stability of the proposed scheme is discussed. Comparisons are made with analytic solutions and with finite difference calculations at selected times. Interaction of two solitary waves with different amplitudes are shown.