Combined variational iteration method with chebyshev wavelet for the solution of convection-diffusion-reaction problem

  • Muhammad Memon Department of Basic Sciences and Related Studies, Quaid-e-Awam University of Engineering, Science and Technology, Nawabshah Sindh Pakistan http://orcid.org/0000-0002-1201-0834
  • Khuda Bux Amur Department of Mathematics and Statistics, Quaid-e-Awam University of Engineering, Science and Technology Nawabshah Sindh Pakistan
  • Wajid Ali Shaikh Department of Mathematics and Statistics, Quaid-e-Awam University of Engineering, Science and Technology Nawabshah Sindh Pakistan

Abstract

The goal of the work is to solve the nonlinear convection-diffusion-reaction problem using the variational iteration method with the combination of the Chebyshev wavelet. This work developed a hybrid iterative technique named as Variational iteration method with the Chebyshev wavelet for the solutions of nonlinear convection-diffusion-reaction problems. The aim of applying the derived algorithm is to achieve fast convergence. During the solution of the given problem, the restricted variations will be mathematically justified. The effects of the scaling and other parameters like diffusion parameter, convection parameter, and reaction parameter on the solution are also focused on by their suitable selection. The approximate results include the error profiles and the simulations. The results of variational iteration with the Chebyshev wavelet are compared with variational iteration method, the Modified variational iteration method, and the Variational iteration method with Legendre wavelet. The error profiles allow us to compare the results with well-known existing schemes.

Published
Apr 3, 2023
How to Cite
MEMON, Muhammad; AMUR, Khuda Bux; SHAIKH, Wajid Ali. Combined variational iteration method with chebyshev wavelet for the solution of convection-diffusion-reaction problem. Mehran University Research Journal of Engineering and Technology, [S.l.], v. 42, n. 2, p. 93-107, apr. 2023. ISSN 2413-7219. Available at: <https://publications.muet.edu.pk/index.php/muetrj/article/view/2586>. Date accessed: 24 may 2024. doi: http://dx.doi.org/10.22581/muet1982.2302.11.
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Articles
This is an open Access Article published by Mehran University of Engineering and Technolgy, Jamshoro under CCBY 4.0 International License