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

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