# A computational modeling of two dimensional reaction–diffusion Brusselator system arising in chemical processes

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## Abstract

In this article, the authors proposed a modified cubic B-spline differential quadrature method (MCB-DQM) to show computational modeling of two-dimensional reaction–diffusion Brusselator system with Neumann boundary conditions arising in chemical processes. The system arises in the mathematical modeling of chemical systems such as in enzymatic reactions, and in plasma and laser physics in multiple coupling between modes. The MCB-DQM reduced the Brusselator system into a system of nonlinear ordinary differential equations. The obtained system of nonlinear ordinary differential equations is then solved by a four-stage RK4 scheme. Accuracy and efficiency of the proposed method successfully tested on four numerical examples and obtained results satisfy the well known result that for small values of diffusion coefficient, the steady state solution converges to equilibrium point \((B,A/B)\) if \(1-A+B^{2}>0\).

## Keywords

Two-dimensional reaction–diffusion Brusselator system Cubic B-spline functions Modified cubic B-spline differential quadrature method System of ordinary differential equations Runge–Kutta 4th order method## Notes

### Acknowledgments

The authors are very thankful to the reviewers for their valuable suggestions to improve the quality of the paper.

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