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

175 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

Access to Document

10.1007/s00211-006-0045-y

Cite this

@article{a5a96d4fa52943ed9ce1a5fe0c5e0ced,

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.",

author = "William McLean and Kassem Mustapha",

year = "2007",

month = jan,

doi = "10.1007/s00211-006-0045-y",

language = "English",

volume = "105",

pages = "481--510",

journal = "Numerische Mathematik",

issn = "0029-599X",

publisher = "Springer New York",

number = "3",

}

TY - JOUR

T1 - A second-order accurate numerical method for a fractional wave equation

AU - McLean, William

AU - Mustapha, Kassem

PY - 2007/1

Y1 - 2007/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=33845751607&partnerID=8YFLogxK

U2 - 10.1007/s00211-006-0045-y

DO - 10.1007/s00211-006-0045-y

M3 - Article

AN - SCOPUS:33845751607

SN - 0029-599X

VL - 105

SP - 481

EP - 510

JO - Numerische Mathematik

JF - Numerische Mathematik

IS - 3

ER -

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

Abstract

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this