A computational study of two-dimensional reaction–diffusion Brusselator system with applications in chemical processes

Abstract

In this paper, an effective numerical technique based on Lucas and Fibonacci polynomials coupled with finite differences is developed for the solution of nonlinear reaction–diffusion Brusselator system. The system arises in modeling of chemical processes such as enzymatic reactions, plasma and laser physics in multiple coupling between modes and in the formation of ozone by atomic oxygen via a triple collision. The proposed scheme first converts the problem to discrete form and then with a collocation approach to a system of linear equations which is easily solvable. Performance of the method is checked by solving one- and two-dimensional test problems. Validation of the results is examined in terms of L∞,L2 and relative error LR norms. In case of no exact solution, quality of computed solution is examined for small value of diffusion coefficient η. It is observed that when 1-ξ+β>0, the solutions converges to equilibrium points (β,ξ/β).