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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]

Although some numerical methods of the Lorenz system have been announced, simple and efficient methods have always been the direction that scholars strive to pursue. Based on this problem, this paper introduces a novel numerical method to solve the Lorenz-type chaotic system which is based on barycentric Lagrange interpolation collocation method (BLICM). The system (1) is adopted as an example to elucidate the solution process. Numerical simulations are used to verify the effectiveness of the present method. [ABSTRACT FROM AUTHOR]

Reproducing kernel Hilbert space method (RKHSM) is an effective method. This paper, for the first time, uses the traditional RKHSM for solving the temperature field in two phase flows of multilayer water injection well. According to 2D oil-water temperature field mathematical model of two phase flows in cylindrical coordinates, selecting the properly initial and boundary conditions, by the process of Gram-Schmidt orthogonalization, the analytical solution was given by reproducing kernel functions in a series expansion form, and the approximate solution was expressed by n-term summation. The satisfied numerical results were carried out by Mathematica 7.0, showing that the larger the difference between injected water temperature and initial borehole temperature or water injection conditions, the more obvious the indication of water accepting zones. The numerical examples evidence the feasibility and effectiveness of the proposed method of the two phase flows in engineering. [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]