Algorithm

Discretization

Applied mathematics

Convergence (economics)

Stability (learning theory)

Economics

Computer science

Extrapolation

Dentistry

Gray (unit)

Radiology

Calculus (dental)

Mathematics

Mathematical analysis

Numerical analysis

Medicine

Economic growth

Richardson extrapolation

Fractional calculus

Runge–Kutta methods

Machine learning

Applied Mathematics Letters

The Gray-Scott model is the representative bistable system in many reaction–diffusion models. Numerical simulation of this model is very difficult especially for space fractional case. In this paper, a novel numerical approach is introduced. We introduce the Runge–Kutta method for time discretization and Fourier transform for spatial discretization. The error has been reduced effectively by using Richardson Extrapolation. We perform stability and convergence analysis for the present method. Numerical experiments show that present method has low computational complexity and higher precision. Long time diffusion behavior of pattern can be observed.

A high-precision numerical approach to solving space fractional Gray-Scott model