High-order algorithms for riesz derivative and their applications (IV)
-
Hengfei Ding
and
Changpin Li
Abstract
The main goal of this article is to establish a new 4th-order numerical differential formula to approximate Riesz derivatives which is obtained by means of a newly established generating function. Then the derived formula is used to solve the Riesz space fractional advection-dispersion equation. Meanwhile, by the energy method, it is proved that the difference scheme is unconditionally stable and convergent with order 𝓞(τ2 + h4). Finally, several numerical examples are given to show that the numerical convergence orders of the numerical differential formulas and the finite difference scheme are in line with the theoretical analysis.
This paper is dedicated to the memory of late Professor Wen Chen
Acknowledgements
The work was partially supported by the National Natural Science Foundation of China (Grant Nos. 11561060, 11671251 and 11961057).
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© 2019 Diogenes Co., Sofia
Articles in the same Issue
- Frontmatter
- Editorial Note
- FCAA special issue – In memory of late professor Wen Chen (FCAA–Volume 22–6–2019)
- Survey Paper
- State-of-art survey of fractional order modeling and estimation methods for lithium-ion batteries
- An investigation on continuous time random walk model for bedload transport
- Tutorial Survey
- Porous functions
- Research Paper
- A time-space Hausdorff derivative model for anomalous transport in porous media
- High-order algorithms for riesz derivative and their applications (IV)
- Mass-conserving tempered fractional diffusion in a bounded interval
- Dispersion analysis for wave equations with fractional Laplacian loss operators
- Lagrangian solver for vector fractional diffusion in bounded anisotropic aquifers: Development and application
- Some further results of the laplace transform for variable–order fractional difference equations
- Robust stability analysis of LTI systems with fractional degree generalized frequency variables
- Discovering a universal variable-order fractional model for turbulent Couette flow using a physics-informed neural network
Articles in the same Issue
- Frontmatter
- Editorial Note
- FCAA special issue – In memory of late professor Wen Chen (FCAA–Volume 22–6–2019)
- Survey Paper
- State-of-art survey of fractional order modeling and estimation methods for lithium-ion batteries
- An investigation on continuous time random walk model for bedload transport
- Tutorial Survey
- Porous functions
- Research Paper
- A time-space Hausdorff derivative model for anomalous transport in porous media
- High-order algorithms for riesz derivative and their applications (IV)
- Mass-conserving tempered fractional diffusion in a bounded interval
- Dispersion analysis for wave equations with fractional Laplacian loss operators
- Lagrangian solver for vector fractional diffusion in bounded anisotropic aquifers: Development and application
- Some further results of the laplace transform for variable–order fractional difference equations
- Robust stability analysis of LTI systems with fractional degree generalized frequency variables
- Discovering a universal variable-order fractional model for turbulent Couette flow using a physics-informed neural network
