Non-polynomial spline method for computational study of reaction diffusion system

Abstract

This work addresses an efficient and new numerical technique utilizing non-polynomial splines to solve system of reaction diffusion equations (RDS). These system of equations arise in pattern formation of some special biological and chemical reactions. Different types of RDS are in the form of spirals, hexagons, stripes, and dissipative solitons. Chemical concentrations can travel as waves in reaction-diffusion systems, where wave like behaviour can be seen. The purpose of this research is to develop a stable, highly accurate and convergent scheme for the solution of aforementioned model. The method proposed in this paper utilizes forward difference for time discretization whereas for spatial discretization cubic non-polynomial spline is used to get approximate solution of the system under consideration. Furthermore, stability of the scheme is discussed via Von-Neumann criteria. Different orders of convergence is achieved for the scheme during a theoretical convergence test. Suggested method is tested for performance on various well known models such as, Brusselator, Schnakenberg, isothermal as well as linear models. Accuracy and efficiency of the scheme is checked in terms of relative error (E R ) and L ∞ norms for different time and space step sizes. The newly obtained results are analyzed and compared with those available in literature.