A semi-analytical method to solve family of Kuramoto–Sivashinsky equations

Abstract

In this article, a semi-analytical technique is implemented to solve Kuramoto–Sivashinsky equations. The present method is the combination of two well-known methods namely Laplace transform method and variational iteration method. This hybrid property of the proposed method reduces the numbers of calculations and materials. The accuracy and applicability of the suggested method is confirmed through illustration examples. The accuracy of the proposed method is described in terms of absolute error. It is investigated through graphs and tables that the Laplace transformation and variational iteration method (LVIM) solutions are in good agreement with the exact solution of the problems. The LVIM solutions are also obtained at different fractional-order of the derivative. It is observed through graphs and tables that the fractional-order solutions are convergent to an integer solution as fractional-orders approaches to an integer-order of the problems. In conclusion, the overall implementation of the present method support the validity of the suggested method. Due to simple, straightforward and accurate implementation, the present method can be extended to other non-linear fractional partial differential equations.