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Novel numerical analysis for nonlinear advection–reaction–diffusion systems

Novel numerical analysis for nonlinear advection–reaction–diffusion systems AbstractIn 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Open Physics de Gruyter

Novel numerical analysis for nonlinear advection–reaction–diffusion systems

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References (28)

Publisher
de Gruyter
Copyright
© 2020 Naveed Shahid et al., published by De Gruyter
ISSN
2391-5471
eISSN
2391-5471
DOI
10.1515/phys-2020-0011
Publisher site
See Article on Publisher Site

Abstract

AbstractIn 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.

Journal

Open Physicsde Gruyter

Published: May 20, 2020

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