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Journal of Scientific Computing
Erschienen in: Journal of Scientific Computing 2/2017

16.11.2016

High-Order Numerical Algorithms for Riesz Derivatives via Constructing New Generating Functions

verfasst von: Hengfei Ding, Changpin Li

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2017

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Abstract

A class of high-order numerical algorithms for Riesz derivatives are established through constructing new generating functions. Such new high-order formulas can be regarded as the modification of the classical (or shifted) Lubich’s difference ones, which greatly improve the convergence orders and stability for time-dependent problems with Riesz derivatives. In rapid sequence, we apply the 2nd-order formula to one-dimension Riesz spatial fractional partial differential equations to establish an unconditionally stable finite difference scheme with convergent order \({\mathcal {O}}(\tau ^2+h^2)\), where \(\tau \) and h are the temporal and spatial stepsizes, respectively. Finally, some numerical experiments are performed to confirm the theoretical results and testify the effectiveness of the derived numerical algorithms.
Vorheriger Artikel Detecting Edges from Non-uniform Fourier Data Using Fourier Frames
Nächster Artikel High-Order Numerical Methods for Solving Time Fractional Partial Differential Equations

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Metadaten
Titel
High-Order Numerical Algorithms for Riesz Derivatives via Constructing New Generating Functions
verfasst von
Hengfei Ding
Changpin Li
Publikationsdatum
16.11.2016
Verlag
Springer US
Erschienen in
Journal of Scientific Computing / Ausgabe 2/2017
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-016-0317-3

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