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Spatio-Temporal Numerical Modeling of Auto-Catalytic Brusselator Model

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2019

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Editura Academiei Romane

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Abstract

The main objective of this article is to propose a chaos free explicit finite-difference (FD) scheme to find the numerical solution for the Brusselator reaction-diffusion model. The scheme is unconditionally stable and it is unconditionally dynamically consistent with the positivity property of continuous model as unknown quantities of auto-catalytic Brusselator system describe the concentrations of two reactant substances. Stability of the proposed FD method is showed with the help of Neumann criteria of stability. Taylor series is used to validate the consistency of the proposed FD method. Forward Euler explicit FD approach and semi-implicit Crank-Nicolson FD scheme are also applied to solve the Brusselator reaction-diffusion system and to make the comparison with the proposed FD scheme.

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Auto-Catalytic Chemical Reaction, Structure Preserving Scheme, Consistency, Von Neumann Stability Analysis, Numerical Simulations

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Ahmed, Nauman...et al. (2019). "Spatio-Temporal Numerical Modeling of Auto-Catalytic Brusselator Model", Romanian Journal of Physics, Vol. 64.

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Romanian Journal of Physics

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64

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