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This paper introduces a numerical approach for the fractional-order Rössler chaotic systems and gives error analysis. The effectiveness of the present method is determined by comparing the numerical results of the high-precision difference scheme and predictor-correctors scheme. Some complex dynamical behaviors for the fractional-order Rössler chaotic systems are shown. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]