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Novel numerical analysis for nonlinear advection–reaction–diffusion systems

Authors
  • Shahid, Naveed1, 2
  • Ahmed, Nauman1
  • Baleanu, Dumitru3, 4, 5
  • Alshomrani, Ali Saleh6
  • Iqbal, Muhammad Sajid2
  • Rehman, Muhammad Aziz-ur1
  • Shaikh, Tahira Sumbal7
  • Rafiq, Muhammad8
  • 1 Department of Mathematics, University of Management and Technology, Pakistan , (Pakistan)
  • 2 Department of Mathematics and Statistics, The University of Lahore, Pakistan , (Pakistan)
  • 3 Department of Mathematics, Cankaya University, 06530, Balgat , (Turkey)
  • 4 ; Institute of Space Sciences, Romania , (Romania)
  • 5 Department of Medical Research, China Medical University Hospital, China Medical University, Taiwan , (China)
  • 6 Faculty of Science, Department Mathematics, King Abdulaziz University, Saudi Arabia , (Saudi Arabia)
  • 7 Department of Mathematics, Lahore College for Women University, Pakistan , (Pakistan)
  • 8 Faculty of Engineering, University of Central Punjab, Pakistan , (Pakistan)
Type
Published Article
Journal
Open Physics
Publisher
Versita
Publication Date
May 20, 2020
Volume
18
Issue
1
Pages
112–125
Identifiers
DOI: 10.1515/phys-2020-0011
Source
De Gruyter
Keywords
License
Green

Abstract

In this article, a numerical model for a Brusselator advection–reaction–diffusion (BARD) system by using an elegant numerical scheme is developed. The consistency and stability of the proposed scheme is demonstrated. Positivity preserving property of the proposed scheme is also verified. The designed scheme is compared with the two well-known existing classical schemes to validate the certain physical properties of the continuous system. A test problem is also furnished for simulations to support our claim. Prior to computations, the existence and uniqueness of solutions for more generic problems is investigated. In the underlying system, the nonlinearities depend not only on the desired solution but also on the advection term that reflects the pivotal importance of the study.

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