A second-order accurate numerical method for a fractional wave equation

William McLean; Kassem Mustapha

doi:10.1007/s00211-006-0045-y

A second-order accurate numerical method for a fractional wave equation

William McLean^*, Kassem Mustapha

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

182 Scopus citations

Abstract

We study a generalized Crank-Nicolson scheme for the time discretization of a fractional wave equation, in combination with a space discretization by linear finite elements. The scheme uses a non-uniform grid in time to compensate for the singular behaviour of the exact solution at t = 0. With appropriate assumptions on the data and assuming that the spatial domain is convex or smooth, we show that the error is of order k ² + h ², where k and h are the parameters for the time and space meshes, respectively.

Original language	English
Pages (from-to)	481-510
Number of pages	30
Journal	Numerische Mathematik
Volume	105
Issue number	3
DOIs	https://doi.org/10.1007/s00211-006-0045-y
State	Published - Jan 2007

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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title = "A second-order accurate numerical method for a fractional wave equation",

abstract = "We study a generalized Crank-Nicolson scheme for the time discretization of a fractional wave equation, in combination with a space discretization by linear finite elements. The scheme uses a non-uniform grid in time to compensate for the singular behaviour of the exact solution at t = 0. With appropriate assumptions on the data and assuming that the spatial domain is convex or smooth, we show that the error is of order k 2 + h 2, where k and h are the parameters for the time and space meshes, respectively.",

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AB - We study a generalized Crank-Nicolson scheme for the time discretization of a fractional wave equation, in combination with a space discretization by linear finite elements. The scheme uses a non-uniform grid in time to compensate for the singular behaviour of the exact solution at t = 0. With appropriate assumptions on the data and assuming that the spatial domain is convex or smooth, we show that the error is of order k 2 + h 2, where k and h are the parameters for the time and space meshes, respectively.

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DO - 10.1007/s00211-006-0045-y

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EP - 510

JO - Numerische Mathematik

JF - Numerische Mathematik

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A second-order accurate numerical method for a fractional wave equation

Abstract

ASJC Scopus subject areas

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