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 (μ, λ/ μ) if 1 - λ+ μ2> 0.

Original languageEnglish
Pages (from-to)1543-1566
Number of pages24
JournalJournal of Mathematical Chemistry
Volume56
Issue number6
DOIs
Publication statusPublished - 1 Jun 2018

Fingerprint

Reaction-diffusion Model
Pattern Formation
Collision
Numerical Simulation
Computer simulation
Differential Quadrature
Cubic B-spline
B-spline Function
Plasma Physics
Ozone
Chemical Processes
Steady-state Solution
Runge-Kutta Methods
Neumann Boundary Conditions
System of Ordinary Differential Equations
Equilibrium Point
Diffusion Coefficient
Convert
Oxygen
Laser modes

Keywords

  • Modified trigonometric cubic B-spline differential quadrature method
  • Reaction–diffusion Brusselator system
  • Runge–Kutta 4 order
  • Trigonometric cubic B-spline functions

Cite this

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title = "Numerical simulation to study the pattern formation of reaction–diffusion Brusselator model arising in triple collision and enzymatic",
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 (μ, λ/ μ) if 1 - λ+ μ2> 0.",
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Numerical simulation to study the pattern formation of reaction–diffusion Brusselator model arising in triple collision and enzymatic. / Alqahtani, Aisha M.

In: Journal of Mathematical Chemistry, Vol. 56, No. 6, 01.06.2018, p. 1543-1566.

Research output: Contribution to journalArticleResearchpeer-review

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AB - 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 (μ, λ/ μ) if 1 - λ+ μ2> 0.

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