Numerical solution of the Korteweg-de Vries (KdV) equation

A numerical method is developed for solving the Korteweg-de Vries (KdV) equation ut − 6uux + uxxx = 0 by using splitting method and quintic spline approximation technique. The convergence, stability and accuracy of the proposed method are discussed. Further, the method is extended to solve the perturbed KdV equation, perturbed by energy influxes of cubic polynomial type, Burgerʹs type and periodic forcing type, and the effects of these influxes on soliton solution are obtained.