Numerical solution to the Gray-Scott Reaction-Diffusion equation using Hyperbolic B-spline

Abstract

AbstractIn the present paper, the one-dimensional Gray-Scott Reaction-diffusion equation is solved numerically with the usage of Hyperbolic B-spline along with the differential quadrature method. The hyperbolic B-spline is used to discretize the partial derivatives, by which the ordinary differential equations will be obtained which further are solved with the SSP-RK43 scheme. The efficiency and accuracy of the method are to be checked by usingL∞andL2errors. The obtained numerical results are shown with help of 2D and 3D figures. As a deduction, it is concluded that the method is an efficient and effective technique for elucidating the Gray-Scott Reaction-diffusion equation and likewise for the variety of partial differential equations.