A stable explicitly solvable numerical method for the Riesz fractional advection-dispersion equations

DOI10.1016/j.amc.2018.03.060zbMath1427.65200OpenAlexW2795458316MaRDI QIDQ2333239

Jingyuan Zhang

Publication date: 12 November 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2018.03.060

zbMATH Keywords

error estimatesfinite difference schemeunconditional stableasymmetric techniqueRiesz fractional advection-dispersion equations

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Fractional partial differential equations (35R11)

Related Items (2)

The solution of direct and inverse fractional advection-dispersion problems by using orthogonal collocation and differential evolution ⋮ High-order finite difference method based on linear barycentric rational interpolation for Caputo type sub-diffusion equation

Uses Software

• JDQR
• JDQZ
• FODE

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stability and convergence of a new finite volume method for a two-sided space-fractional diffusion equation
• A semi-alternating direction method for a 2-D fractional Fitzhugh-Nagumo monodomain model on an approximate irregular domain
• New numerical methods for the Riesz space fractional partial differential equations
• High order unconditionally stable difference schemes for the Riesz space-fractional telegraph equation
• A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula
• Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
• Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation
• Finite difference approximations for a fractional advection diffusion problem
• A new explicit method for the diffusion-convection equation
• Alternating difference block methods and their difference graphs
• Chaos, fractional kinetics, and anomalous transport
• Finite difference approximations for fractional advection-dispersion flow equations
• A direct \(O(N \log ^{2} N)\) finite difference method for fractional diffusion equations
• Stability and convergence of a finite volume method for the space fractional advection-dispersion equation
• Finite difference methods for two-dimensional fractional dispersion equation
• Finite difference approximations for two-sided space-fractional partial differential equations
• The fundamental solution and numerical solution of the Riesz fractional advection-dispersion equation
• Group explicit methods for parabolic equations
• Difference Graphs of Block ADI Method
• Templates for the Solution of Algebraic Eigenvalue Problems
• Fractional kinetic equations: solutions and applications
• Spectral Optimization Methods for the Time Fractional Diffusion Inverse Problem
• Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations
• A Crank--Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation
• Uniformly Stable Explicitly Solvable Finite Difference Method for Fractional Diffusion Equations
• Existence and Uniqueness of the Weak Solution of the Space-time Fractional Diffusion Equation and a Spectral Method Approximation
• Finite Element Method for the Space and Time Fractional Fokker–Planck Equation
• Numerical Approximation of a Time Dependent, Nonlinear, Space‐Fractional Diffusion Equation
• Computational method for solving space fractional Fisher's nonlinear equation
• A numerical approach for the Riesz space-fractional Fisher' equation in two-dimensions

This page was built for publication: A stable explicitly solvable numerical method for the Riesz fractional advection-dispersion equations