Efficient numerical algorithms for Riesz-space fractional partial differential equations based on finite difference/operational matrix
type: Item
instance of: scholarly article
title: Efficient numerical algorithms for Riesz-space fractional partial differential equations based on finite difference/operational matrix
zbMATH Open document ID: 1475.65081
author: Nikhil Srivastava
author: A. Singh
author: Yashveer Kumar
author: Vineet Kumar Singh
published in: Applied Numerical Mathematics
publication date: 2021-02-15T00:00:00Z
review text: The paper is concerned with initial-boundary value problems for linear PDEs with first order time derivative and fractional space derivatives of Riesz type on a bounded interval. Depending on whether one or (a sum of) two such fractional derivatives of appropriate orders occur, the equation is interpreted as a ``Riesz space fractional diffusion equation'' or a ``Riesz space fractional advection-dispersion equation'', respectively. Numerical methods are proposed to compute approximations to both types of problems, using a finite difference scheme based on the ``matrix transform method'' for spatial discretizations and an ``operational matrix method'' for time discretization. Questions of convergence order and stability are discussed, and some numerical experiments are carried out for illustration.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 42C10
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 35R11
zbMATH DE Number: 7310817
zbMATH Keywords: Riesz-space fractional diffusion equation
zbMATH Keywords: Riesz-space fractional advection-dispersion equation
zbMATH Keywords: matrix transform method
zbMATH Keywords: operational matrix
zbMATH Keywords: optimal error bound
zbMATH Keywords: unconditional stability
reviewed by: Michael Plum
describes a project that uses: FODE
MaRDI profile type: Publication
full work available at URL: j.apnum.2020.10.032
OpenAlex ID: W3104894184
Wikidata QID: Q115360361
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DOI: 10.1016/J.APNUM.2020.10.032