An Analytical Approach to the New Solution of Family of Kuramoto Sivashinsky Equation by q-Homotopy Analysis Technique
This article is part of Special Issue:
Abdullah Shah,
Safdar Hussain,
Abdullah Shah
Department of Mathematics , King Fahd University of Petroleum and Minerals (KFUPM) , Dhahran , 31261 , Saudi Arabia , kfupm.edu.sa
Interdisciplinary Research Center for Refining and Advanced Chemicals , KFUPM , Dhahran , 31261 , Saudi Arabia , kfupm.edu.sa
Search for more papers by this authorCorresponding Author
Safdar Hussain
Department of Mathematical Sciences , Karakoram International University Main Campus , Gilgit , 15100 , Pakistan
Search for more papers by this authorAbdullah Shah,
Safdar Hussain,
Abdullah Shah
Department of Mathematics , King Fahd University of Petroleum and Minerals (KFUPM) , Dhahran , 31261 , Saudi Arabia , kfupm.edu.sa
Interdisciplinary Research Center for Refining and Advanced Chemicals , KFUPM , Dhahran , 31261 , Saudi Arabia , kfupm.edu.sa
Search for more papers by this authorCorresponding Author
Safdar Hussain
Department of Mathematical Sciences , Karakoram International University Main Campus , Gilgit , 15100 , Pakistan
Search for more papers by this authorAcademic Editor: Md. Kamrujjaman
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.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Open Research
Data Availability
Data sharing is not applicable to this article as no new data were created or analyzed in this study.
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