Convergence analysis of high-order compact alternating direction implicit schemes for the two-dimensional time fractional diffusion equation
type: Item
instance of: scholarly article
title: Convergence analysis of high-order compact alternating direction implicit schemes for the two-dimensional time fractional diffusion equation
zbMATH Open document ID: 1264.65143
published in: Numerical Algorithms
publication date: 2013-03-27T00:00:00Z
review text: The author proposes a pair of compact alternating direction implicit schemes, I and II, for solving a two-dimensional time fractional diffusion equation describing subdiffusive phenomena with a nonhomogeneous term. Scheme I is obtained by replacing the value of the current time level with the previous one. The stability and accuracy of scheme I are investigated. Scheme I has the advantage of high accuracy with the coefficient matrix still being tridiagonal; therefore, the linear system of equations is easy to solve efficiently to a high accuracy. It is also shown that scheme I is unconditionally stable and convergent. Depending on the value of the parameter \(\gamma\in(0,1)\) in the Caputo fractional derivative \(_0^CD_t^\gamma u\) of the function \(u(x, y, t)\) making the left hand-side term of the given diffusion equation, scheme I is good for \(\gamma\in[1/2,1)\). Scheme II, which comes with a correction term, is more suitable for \(\gamma\in[0,1/2)\). The theoretical analysis is verified by some numerical experiments.
reviewed by: Rémi Vaillancourt
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35R11
zbMATH DE Number: 6148998
zbMATH Keywords: multidimensional fractional differential equation
zbMATH Keywords: compact scheme
zbMATH Keywords: finite difference
zbMATH Keywords: alternating direction implicit
zbMATH Keywords: stability
zbMATH Keywords: convergence
zbMATH Keywords: fractional diffusion equation
zbMATH Keywords: Caputo fractional derivative
zbMATH Keywords: numerical experiments
author: Mingrong Cui
describes a project that uses: ma2dfc
MaRDI profile type: Publication
full work available at URL: s11075-012-9589-3
OpenAlex ID: W2104575663
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DOI: 10.1007/S11075-012-9589-3
description: scientific article; zbMATH DE number 6148998