Numerical solution of Korteweg–de Vries-Burgers equation by the modified variational iteration algorithm-II arising in shallow water waves

In this paper, an effective modification of variational iteration algorithm-II is presented for the numerical solution of the Korteweg–de Vries-Burgers equation, Burgers equation and Kortewege–de Vries equation. In this modification, an auxiliary parameter is introduced which make sure the convergence of the standard algorithm-II. In order to assess the precision of the solutions, numerical computations obtained from the time evaluation of the solutions of the Kortewege–de Vries-Burgers equation with different values for dispersion and diffusion coefficients, show that the proposed algorithm converges rapidly, yields accurate results and offers better accuracy and robustness in comparison with other previous numerical methods. Furthermore, the method can be readily implemented for illuminating viably an enormous number of nonlinear differential equations with better accuracy. Furthermore, any transformation, weak nonlinearity assumption to find an explicit solution or any discretization to find the numerical solution is not necessary for this proposed algorithm. (paper)