Numerical simulation of reaction-diffusion systems by modified cubic B-spline differential quadrature method. (November 2016)

• Record Type: Journal Article
• Authors: Mittal, R.C.; Rohila, Rajni
• Is Part Of: Chaos, solitons and fractals. Volume 92(2016)
• Page Start: 9
• Page End: 19
• Publication Date: 2016-11
• Subjects: Reaction-diffusion systems -- Differential quadrature method -- Cubic B-spline basis functions -- Runge Kutta method -- Thomas algorithm; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2016.09.007
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: In this paper, we have applied modified cubic B-spline based differential quadrature method to get numerical solutions of one dimensional reaction-diffusion systems such as linear reaction-diffusion system, Brusselator system, Isothermal system and Gray-Scott system. The models represented by these systems have important applications in different areas of science and engineering. The most striking and interesting part of the work is the solution patterns obtained for Gray Scott model, reminiscent of which are often seen in nature. We have used cubic B-spline functions for space discretization to get a system of ordinary differential equations. This system of ODE's is solved by highly stable SSP-RK43 method to get solution at the knots. The computed results are very accurate and shown to be better than those available in the literature. Method is easy and simple to apply and gives solutions with less computational efforts.