High-order algorithms for Riesz derivative and their applications. II
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Publication:349923
DOI10.1016/j.jcp.2014.06.007zbMath1349.65284OpenAlexW1969734198MaRDI QIDQ349923
Changpin Li, Heng-Fei Ding, Yang Quan Chen
Publication date: 5 December 2016
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2014.06.007
Riemann-Liouville derivativeGrünwald-Letnikov derivativehigh-order unconditionally-stable algorithmspatial Riesz fractional reaction-dispersion equation
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) Numerical differentiation (65D25) Fractional partial differential equations (35R11)
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III
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Exponentially accurate spectral and spectral element methods for fractional ODEs
- Numerical methods and analysis for a class of fractional advection-dispersion models
- A second order explicit finite difference method for the fractional advection diffusion equation
- Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
- New numerical methods for the Riesz space fractional partial differential equations
- High-order finite element methods for time-fractional partial differential equations
- Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion
- Riesz potential operators and inverses via fractional centred derivatives
- Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
- Matrix approach to discrete fractional calculus. II: Partial fractional differential equations
- High-order algorithms for Riesz derivative and their applications. I.
- The accuracy and stability of an implicit solution method for the fractional diffusion equation
- A predictor-corrector approach for the numerical solution of fractional differential equations
- Finite difference approximations for fractional advection-dispersion flow equations
- Quasi-compact finite difference schemes for space fractional diffusion 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
- An Efficient Implicit FEM Scheme for Fractional-in-Space Reaction-Diffusion Equations
- Toeplitz Preconditioners for Toeplitz Systems with Nonnegative Generating Functions
- Fractional Spectral Collocation Method
- An Introduction to Iterative Toeplitz Solvers
- Variational formulation for the stationary fractional advection dispersion equation
