A unified numerical scheme for the multi-term time fractional diffusion and diffusion-wave equations with variable coefficients
type: Item
instance of: scholarly article
title: A unified numerical scheme for the multi-term time fractional diffusion and diffusion-wave equations with variable coefficients
zbMATH Open document ID: 1376.65112
author: Hu Chen
author: Shujuan Lü
author: Wenping Chen
published in: Journal of Computational and Applied Mathematics
publication date: 2017-11-03T00:00:00Z
review text: The authors derive a numerical scheme based on the use of a Legendre spectral method in space and a finite difference method in time for multi-term time fractional diffusion and diffusion-wave equations with variable coefficients in a bounded domain. The fractional derivatives are given in Caputo sense. A detailed error analysis is given for the scheme. The convergence rate in \(L^\infty(L^2)\) norm is proved to be \(\mathrm{O}(\tau^2+N^{1-m})\), where \(\tau\), \(N\), and \(m\) are the time-step size, polynomial degree, and regularity in the space variable of the exact solution, respectively. Some numerical examples are presented to support the theoretical results.
reviewed by: Abdallah Bradji
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 35L05
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M15
zbMATH DE Number: 6802838
zbMATH Keywords: fractional diffusion equation
zbMATH Keywords: fractional diffusion-wave equation
zbMATH Keywords: stability
zbMATH Keywords: convergence
zbMATH Keywords: error bounds
zbMATH Keywords: finite difference method in time
zbMATH Keywords: Legendre spectral method in space
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: j.cam.2017.09.011
OpenAlex ID: W2754735025
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DOI: 10.1016/J.CAM.2017.09.011
description: scientific article; zbMATH DE number 6802838