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

DOI10.1016/j.aml.2021.107759OpenAlexW3211132577MaRDI QIDQ2060835

Che Han, Zhi-yuan Li, Yu-Lan Wang

Publication date: 13 December 2021

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2021.107759

zbMATH Keywords

numerical simulationsspatial patternsbistable systemfractional Gray-Scott modelmodified Fourier spectral method

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Reaction-diffusion equations (35K57) NLS equations (nonlinear Schrödinger equations) (35Q55) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractional partial differential equations (35R11)

Related Items

NUMERICAL SIMULATION OF THE FRACTIONAL-ORDER RÖSSLER CHAOTIC SYSTEMS WITH GRÜNWALD–LETNIKOV FRACTIONAL DERIVATIVE ⋮ A numerical approach for solving nonlinear Fredholm integro-differential equation with boundary layer ⋮ Novel patterns in a class of fractional reaction-diffusion models with the Riesz fractional derivative ⋮ A finite difference scheme for the two-dimensional Gray-Scott equation with fractional Laplacian ⋮ High-fidelity simulations for Turing pattern formation in multi-dimensional Gray-Scott reaction-diffusion system ⋮ Numerical simulation of the time fractional Gray-Scott model on 2D space domains using radial basis functions

Cites Work

• Unnamed Item
• Fourier spectral methods for fractional-in-space reaction-diffusion equations
• A second-order operator splitting Fourier spectral method for fractional-in-space reaction-diffusion equations
• General propagation lattice Boltzmann model for a variable-coefficient compound KdV-Burgers equation
• Conservative Fourier spectral method and numerical investigation of space fractional Klein-Gordon-Schrödinger equations
• Rogue wave solutions for a higher-order nonlinear Schrödinger equation in an optical fiber
• \(N\)th-order rogue waves for the \(AB\) system via the determinants
• Dark soliton solutions for a coupled nonlinear Schrödinger system
• Pattern formation in the Gray-Scott model
• Spectral Methods in MATLAB
• Exact Homoclinic and Heteroclinic Solutions of the Gray--Scott Model for Autocatalysis
• NUMERICAL SOLUTIONS OF SPACE FRACTIONAL VARIABLE-COEFFICIENT KdV–MODIFIED KdV EQUATION BY FOURIER SPECTRAL METHOD
• An Algorithm for the Machine Calculation of Complex Fourier Series