Please use this identifier to cite or link to this item:
https://hdl.handle.net/11499/30287
Title: | Efficient numerical treatment of nonlinearities in the advection–diffusion–reaction equations | Authors: | Erdogan, U. Sari, M. Koçak, Hüseyin |
Keywords: | Advection-diffusion-reaction equations Fréchet derivative Hybrid spline difference method Linearization Space discretization Time discretization Advection Algebra Control nonlinearities Diffusion Finite difference method Iterative methods Non Newtonian flow Design/methodology/approach Hybrid spline difference methods Non-linear algebraic system Numerical treatments Reaction equations Space discretizations Numerical methods |
Publisher: | Emerald Group Publishing Ltd. | Abstract: | Purpose: The purpose of this study is to propose a non-classical method to obtain efficient and accurate numerical solutions of the advection–diffusion–reaction equations. Design/methodology/approach: Unlike conventional numerical methods, this study proposes a numerical scheme using outer Newton iteration applied to a time-dependent PDE. The linearized time dependent PDE is discretized by trapezoidal rule, which is second order in time, and by spline-based finite difference method of fourth order in space. Findings: Using the proposed technique, even when relatively large time step sizes are used in computations, the efficiency of the proposed procedure is very clear for the numerical examples in comparison with the existing classical methods. Originality/value: This study, unlike these classical methods, proposes an alternative approach based on linearizing the nonlinear problem at first, and then discretizing it by an appropriate scheme. This technique helps to avoid considering the convergence issues of Newton iteration applied to nonlinear algebraic system containing many unknowns at each time step if an implicit method is used in time discretization. The linearized PDE can be solved by implicit time integrator, which enables the use of large time step size. © 2018, Emerald Publishing Limited. | URI: | https://hdl.handle.net/11499/30287 https://doi.org/10.1108/HFF-05-2017-0198 |
ISSN: | 0961-5539 |
Appears in Collections: | İktisadi ve İdari Bilimler Fakültesi Koleksiyonu Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection |
Show full item record
CORE Recommender
SCOPUSTM
Citations
10
checked on Oct 13, 2024
WEB OF SCIENCETM
Citations
9
checked on Oct 31, 2024
Page view(s)
36
checked on Aug 24, 2024
Google ScholarTM
Check
Altmetric
Items in GCRIS Repository are protected by copyright, with all rights reserved, unless otherwise indicated.