Numerical procedures for recovering a time dependent coefficient in a parabolic differential equation

Hossein Azari; Walter Allegretto; Yanping Lin; Shuhua Zhang

Numerical procedures for recovering a time dependent coefficient in a parabolic differential equation

Hossein Azari, Walter Allegretto, Yanping Lin, Shuhua Zhang

Research output: Journal article publication › Journal article › Academic research › peer-review

Abstract

In this paper we study a finite difference approximation to an inverse problem of finding the function u(x, t) and the unknown positive coefficient a(t) in a parabolic initial-boundary value problem. The backward Euler scheme is studied and its convergence is proved via the application of the discrete maximum principle. Error estimates for u and a, and some experimental numerical results using the newly proposed numerical procedure are presented.

Original language	English
Pages (from-to)	181-199
Number of pages	19
Journal	Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms
Volume	11
Issue number	1-2
Publication status	Published - 1 Feb 2004
Externally published	Yes

Keywords

Convergence
Inverse problem
Maximum principle
Numerical method

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

Cite this

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title = "Numerical procedures for recovering a time dependent coefficient in a parabolic differential equation",

abstract = "In this paper we study a finite difference approximation to an inverse problem of finding the function u(x, t) and the unknown positive coefficient a(t) in a parabolic initial-boundary value problem. The backward Euler scheme is studied and its convergence is proved via the application of the discrete maximum principle. Error estimates for u and a, and some experimental numerical results using the newly proposed numerical procedure are presented.",

keywords = "Convergence, Inverse problem, Maximum principle, Numerical method",

author = "Hossein Azari and Walter Allegretto and Yanping Lin and Shuhua Zhang",

year = "2004",

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day = "1",

language = "English",

volume = "11",

pages = "181--199",

journal = "Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms",

issn = "1492-8760",

publisher = "Watam Press",

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Numerical procedures for recovering a time dependent coefficient in a parabolic differential equation. / Azari, Hossein; Allegretto, Walter; Lin, Yanping et al.
In: Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms, Vol. 11, No. 1-2, 01.02.2004, p. 181-199.

Research output: Journal article publication › Journal article › Academic research › peer-review

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T1 - Numerical procedures for recovering a time dependent coefficient in a parabolic differential equation

AU - Azari, Hossein

AU - Allegretto, Walter

AU - Lin, Yanping

AU - Zhang, Shuhua

PY - 2004/2/1

Y1 - 2004/2/1

N2 - In this paper we study a finite difference approximation to an inverse problem of finding the function u(x, t) and the unknown positive coefficient a(t) in a parabolic initial-boundary value problem. The backward Euler scheme is studied and its convergence is proved via the application of the discrete maximum principle. Error estimates for u and a, and some experimental numerical results using the newly proposed numerical procedure are presented.

AB - In this paper we study a finite difference approximation to an inverse problem of finding the function u(x, t) and the unknown positive coefficient a(t) in a parabolic initial-boundary value problem. The backward Euler scheme is studied and its convergence is proved via the application of the discrete maximum principle. Error estimates for u and a, and some experimental numerical results using the newly proposed numerical procedure are presented.

KW - Convergence

KW - Inverse problem

KW - Maximum principle

KW - Numerical method

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M3 - Journal article

SN - 1492-8760

VL - 11

SP - 181

EP - 199

JO - Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

JF - Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

IS - 1-2

ER -

Numerical procedures for recovering a time dependent coefficient in a parabolic differential equation

Abstract

Keywords

ASJC Scopus subject areas

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