An Analytical Approach to the New Solution of Family of Kuramoto Sivashinsky Equation by q-Homotopy Analysis Technique

Abstract

The current work aims to study a new analytical solution method for a family of Kuramoto–Sivashinsky equation (KSE). For this purpose, we implement the q-homotopy analysis method (q-HAM), a method extensively used due to its easy implementation, fast convergence, and presence of convergence-controlling parameters. This method does not require any transformation, linearization, or discretization. The applied method offers a well-convergent series solution. Results are obtained for some fixed values of physically significant parameters involved in the mathematical model. The computed results are compared with the travelling wave solutions and are illustrated graphically and in tabulated form for absolute error estimation. The comparison reveals the q-HAM provides better results than the existing methods.