An analytical-numerical method for solving the Korteweg-de Vries equation

In this paper, an analytical-numerical method is applied to the one-dimensional Korteweg-de Vries equation with a variant of boundary and initial conditions to obtain its numerical solutions at small times. Two test problem with known exact solutions are studied to demonstrate the accuracy of the present method. The obtained results are compared with the exact solution of each problem and are found to be in good agreement with each other. The numerical scheme is also compared with earlier work and shown to be accurate and efficient.