The space spectral interpolation collocation method for reaction-diffusion systems

Zhang, Xiaoli; Zhang, Wei; Wang, Yulan; Ban, Ting-Ting

doi:10.2298/tsci200402022z

Cited by 4 publications

(1 citation statement)

References 29 publications

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“…In [4][5][6], the authors gave a dynamic analysis of a fractional-order Lorenz chaotic system. Although some numerical and analytical methods of the FDEs have been announced, such as spectral method [7][8][9][10][11], reproducing kernel method [12][13][14][15][16][17][18][19], homotopy perturbation method [20][21][22][23], high-precision numerical approach [24][25][26][27], and so on numerical and analytical methods [28][29][30][31][32][33][34][35][36]. These researchers all say their own approach can accurately simulate chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of the Fractional-Order Lorenz Chaotic Systems with燙aputo Fractional Derivative

Dai¹,

Li²,

Li³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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Although some numerical methods of the fractional-order chaotic systems have been announced, high-precision numerical methods have always been the direction that researchers strive to pursue. Based on this problem, this paper introduces a high-precision numerical approach. Some complex dynamic behavior of fractional-order Lorenz chaotic systems are shown by using the present method. We observe some novel dynamic behavior in numerical experiments which are unlike any that have been previously discovered in numerical experiments or theoretical studies. We investigate the influence of α 1 , α 2 , α 3 on the numerical solution of fractional-order Lorenz chaotic systems. The simulation results of integer order are in good agreement with those of other methods. The simulation results of numerical experiments demonstrate the effectiveness of the present method.

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Section: Introductionmentioning

confidence: 99%

Numerical Simulation of the Fractional-Order Lorenz Chaotic Systems with燙aputo Fractional Derivative

Dai¹,

Li²,

Li³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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Fractal diffusion from a geometric Ricci flow

El-Nabulsi

2022

J Elliptic Parabol Equ

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Reduced Multiplicative (BURA-MR) and Additive (BURA-AR) Best Uniform Rational Approximation Methods and Algorithms for Fractional Elliptic Equations

et al. 2021

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Numerical methods for spectral space-fractional elliptic equations are studied. The boundary value problem is defined in a bounded domain of general geometry, Ω⊂Rd, d∈{1,2,3}. Assuming that the finite difference method (FDM) or the finite element method (FEM) is applied for discretization in space, the approximate solution is described by the system of linear algebraic equations Aαu=f, α∈(0,1). Although matrix A∈RN×N is sparse, symmetric and positive definite (SPD), matrix Aα is dense. The recent achievements in the field are determined by methods that reduce the original non-local problem to solving k auxiliary linear systems with sparse SPD matrices that can be expressed as positive diagonal perturbations of A. The present study is in the spirit of the BURA method, based on the best uniform rational approximation rα,k(t) of degree k of tα in the interval [0,1]. The introduced additive BURA-AR and multiplicative BURA-MR methods follow the observation that the matrices of part of the auxiliary systems possess very different properties. As a result, solution methods with substantially improved computational complexity are developed. In this paper, we present new theoretical characterizations of the BURA parameters, which gives a theoretical justification for the new methods. The theoretical estimates are supported by a set of representative numerical tests. The new theoretical and experimental results raise the question of whether the almost optimal estimate of the computational complexity of the BURA method in the form O(Nlog2N) can be improved.

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The space spectral interpolation collocation method for reaction-diffusion systems

Cited by 4 publications

References 29 publications

Numerical Simulation of the Fractional-Order Lorenz Chaotic Systems with燙aputo Fractional Derivative

Numerical Simulation of the Fractional-Order Lorenz Chaotic Systems with燙aputo Fractional Derivative

Fractal diffusion from a geometric Ricci flow

Reduced Multiplicative (BURA-MR) and Additive (BURA-AR) Best Uniform Rational Approximation Methods and Algorithms for Fractional Elliptic Equations

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