Open Access

ARTICLE

Reliable iterative techniques for solving the KS equation arising in fluid flow

Munirah Alotaibi¹, Doaa Rizk², Amal Al−Hanaya¹, Ahmed Hagag³

1 Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Saudi Arabia
2 Department of Mathematics, College of Science and Arts, Qassim University, Al-Asyah, Saudi Arabia
3 Department of Basic Science, Faculty of Engineering, Sinai University – Kantara Branch, Ismailia, 41636 Egypt

* Corresponding Author: Ahmed Hagag ()

Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería 2024, 40(1), 1-9. https://doi.org/10.23967/j.rimni.2024.02.003

Received 02 January 2024; Accepted 15 February 2024; Issue published 23 February 2024

Abstract

In this study, we examine the Kuramoto-Sivashinsky equation which is a nonlinear model that describes several physical and chemical events arising in fluid flow. The approximate analytical solution for the fractional KS (FKS) problem is calculated using the Temimi-Ansari method (TAM) and the natural decomposition method (NDM). The projected procedure (NDM) combines the adomian decomposition method with the natural transform. Each technique can deal with nonlinear terms without making any assumptions. The methodologies under consideration provide ω_n-curves that display the convergence window of the power series solution that approaches the exact solution. We explore two distinct examples to confirm the efficiency and applicability of the proposed strategies. The acquired outcomes are compared numerically with the q-homotopy analysis transform method (q-HATM). The numerical investigation is carried out to validate the precision and dependability of the approaches under consideration. Additionally, the nature of the outcomes gained has been displayed in a different order. The obtained results show that the proposed techniques are highly efficient and simple to use to analyze the behavior of other nonlinear models.

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Keywords

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