High-Order Algorithms for Riesz Derivative and Their Applications(I)

2014/01/01 by Hengfei Ding, Changpin Li, YangQuan Chen · 1 citation
Mathematics · #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #Differential Equations and Numerical Methods #Mathematics #Algorithm #Order (exchange) #Derivative (finance) #Fractional calculus #Scheme (mathematics) #Applied mathematics #Mathematical analysis

paper · pdf · doi:10.1155/2014/653797

openalex publication_date 2014/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/23

Abstract

We firstly develop the high-order numerical algorithms for the left and right Riemann-Liouville derivatives. Using these derived schemes, we can get high-order algorithms for the Riesz fractional derivative. Based on the approximate algorithm, we construct the numerical scheme for the space Riesz fractional diffusion equation, where a fourth-order scheme is proposed for the spacial Riesz derivative, and where a compact difference scheme is applied to approximating the first-order time derivative. It is shown that the difference scheme is unconditionally stable and convergent. Finally, numerical examples are provided which are in line with the theoretical analysis.

Citations

• An Introduction to Iterative Toeplitz Solvers
• A second-order accurate numerical method for a fractional wave equation

Cited by

• Fractional calculus [wikipedia]

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