A simple similarity-transformation-iterative scheme applied to Korteweg–de Vries equation

摘要

In this paper, we apply a simple iterative scheme and give an algorithm to solve the reduced Korteweg–de Vries equation by a scaled similarity-transformation. The obtained numerical solutions are valid for the whole solution domain. Results obtained by the method have been compared with the solution of Marchant and Smyth [T.R. Marchant, N.F. Smyth, Initial-boundary value problems for the KdV equations, IMA J. Appl. Math. 47 (1991) 247–264] and are found to be in good agreement with each other.