THE FUNDAMENTAL AND NUMERICAL SOLUTIONS OF THE RIESZ SPACE-FRACTIONAL REACTION–DISPERSION EQUATION

DOI10.1017/S1446181108000333zbMath1179.35029OpenAlexW2157401664MaRDI QIDQ5191232

Ian W. Turner, V. V. Anh, Jinghua Chen, Fawang Liu

Publication date: 29 July 2009

Published in: The ANZIAM Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1446181108000333

zbMATH Keywords

fundamental solutionfinite difference approximationLaplace-Fourier transformtransform methodsreaction-dispersion equation

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Fundamental solutions to PDEs (35A08) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Theoretical approximation in context of PDEs (35A35) Fractional partial differential equations (35R11)

Related Items (13)

An efficient parallel algorithm for Caputo fractional reaction-diffusion equation with implicit finite-difference method ⋮ Distributed order reaction-diffusion systems associated with Caputo derivatives ⋮ Two explicit and implicit finite difference schemes for time fractional Riesz space diffusion equation ⋮ Fourth-order numerical method for the Riesz space fractional diffusion equation with a nonlinear source term ⋮ A convergent algorithm for solving higher-order nonlinear fractional boundary value problems ⋮ A spectral Legendre-Gauss-Lobatto collocation method for a space-fractional advection diffusion equations with variable coefficients ⋮ High-order algorithms for Riesz derivative and their applications. I. ⋮ The analytical solution and numerical solution of the fractional diffusion-wave equation with damping ⋮ Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations ⋮ Numerical techniques for simulating a fractional mathematical model of epidermal wound healing ⋮ Improved matrix transform method for the Riesz space fractional reaction dispersion equation ⋮ A parallel algorithm for the Riesz fractional reaction-diffusion equation with explicit finite difference method ⋮ Computational solutions of distributed order reaction-diffusion systems associated with Riemann-Liouville derivatives

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Fractional high order methods for the nonlinear fractional ordinary differential equation
• Approximation of Lévy-Feller diffusion by random walk
• Numerical methods for the solution of partial differential equations of fractional order.
• Numerical solution of the space fractional Fokker-Planck equation.
• Time fractional advection-dispersion equation
• Wright functions as scale-invariant solutions of the diffusion-wave equation
• Finite difference approximations for two-sided space-fractional partial differential equations
• Existence of Turing Instabilities in a Two-Species Fractional Reaction-Diffusion System

This page was built for publication: THE FUNDAMENTAL AND NUMERICAL SOLUTIONS OF THE RIESZ SPACE-FRACTIONAL REACTION–DISPERSION EQUATION