Numerical simulation to study the pattern formation of reaction–diffusion Brusselator model arising in triple collision and enzymatic

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Abstract

This article studies the pattern formation of reaction–diffusion Brusselator model along with Neumann boundary conditions arising in chemical processes. To accomplish this work, a new modified trigonometric cubic B-spline functions based differential quadrature algorithm is developed which is more general than (Mittal and Jiwari in Appl Math Comput 217(12):5404–5415, 2011; Jiwari and Yuan in J Math Chem 52:1535–1551, 2014). The reaction–diffusion model arises in enzymatic reactions, in the formation of ozone by atomic oxygen via a triple collision, and in laser and plasma physics in multiple couplings between modes. The algorithm converts the model into a system of ordinary differential equations and the obtained system is solved by Runge–Kutta method. To check the precision and performance of the proposed algorithm four numerical problems are contemplated and computed results are compared with the existing methods. The computed results pamper the theory of Brusselator model that for small values of diffusion coefficient, the steady state solution converges to equilibrium point \(( {\mu , \lambda /\mu })\) if \(1-\lambda +\mu ^{2}>0\).

Keywords

Reaction–diffusion Brusselator system Trigonometric cubic B-spline functions Modified trigonometric cubic B-spline differential quadrature method Runge–Kutta \(4^{\mathrm{th}}\) order 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematical Sciences Department, College of SciencesPrincess Nourah Bint Abdulrahman UniversityRiyadhSaudi Arabia

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