Mathematical analysis and numerical simulation of two-component system with non-integer-order derivative in high dimensions

Advances in Difference Equations

Kolade M Owolabi¹  Abdon Atangana¹ 

[1] Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa

关键词: Fourier spectral method;    exponential integrator;    fractional reaction-diffusion;    nonlinear PDEs;    numerical simulations;    Turing instability;    34A34;    35A05;    35K57;    65L05;    65M06;    93C10;   

DOI  :  10.1186/s13662-017-1286-z

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we propose efficient and reliable numerical methods to solve two notable non-integer-order partial differential equations. The proposed algorithm adapts the Fourier spectral method in space, coupled with the exponential integrator scheme in time. As an advantage over existing methods, our method yields a full diagonal representation of the non-integer fractional operator, with better accuracy over a finite difference scheme. We realize in this work that evolution equations formulated in the form of fractional-in-space reaction-diffusion systems can result in some amazing examples of pattern formation. Numerical experiments are performed in two and three space dimensions to justify the theoretical results. Simulation results revealed that pattern formation in a fractional medium is practically the same as in classical reaction-diffusion scenarios.

【 授权许可】

CC BY