Numerical method for the simultaneous determination of unknown parameters in a parabolic equation

被引：6

作者：

Yang, Runsheng ^{[1
]}

Li, Yijun ^{[1
]}

机构：

[1] Changsha Univ Sci & Technol, Coll Math, Changsha, Hunan, Peoples R China

来源：

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS | 2010年 / 87卷 / 01期

关键词：

inverse parabolic problem; unknown parameter; finite difference scheme; least square method; HEAT-CONDUCTION PROBLEM; INVERSE PROBLEM; P(T);

D O I：

10.1080/00207160801979199

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Numerical procedures for the solution of an inverse problem of simultaneously determining unknown parameters in a linear parabolic equation are considered. The approach proposed is to approximate unknown functions using Chebyshev polynomials, which are determined consecutively from the solutions of the minimization problems based on overspecified data. Finally, the results of a numerical experiment are displayed.

引用

页码：150 / 157

页数：8

共 17 条

[1] Beck J.V., 1985, Inverse Heat Conduction: Ill-Posed Problems
[2] Cannon J. R., 1992, Meccanica, V27, P85, DOI 10.1007/BF00420586
[3] PARAMETER DETERMINATION IN PARABOLIC PARTIAL-DIFFERENTIAL EQUATIONS FROM OVERSPECIFIED BOUNDARY DATA
CANNON, JR
ZACHMANN, D
[J]. INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 1982, 20 (06) : 779 - 788
[4] NUMERICAL PROCEDURES FOR THE DETERMINATION OF AN UNKNOWN COEFFICIENT IN SEMILINEAR PARABOLIC DIFFERENTIAL-EQUATIONS
CANNON, JR
LIN, YP
XU, SZ
[J]. INVERSE PROBLEMS, 1994, 10 (02) : 227 - 243
[5] AN INVERSE PROBLEM OF FINDING A PARAMETER IN A SEMILINEAR HEAT-EQUATION
CANNON, JR
LIN, YP
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1990, 145 (02) : 470 - 484
[6] DETERMINATION OF PARAMETER P(T) IN HOLDER CLASSES FOR SOME SEMILINEAR PARABOLIC EQUATIONS
CANNON, JR
LIN, YP
[J]. INVERSE PROBLEMS, 1988, 4 (03) : 595 - 606
[7] DETERMINATION OF A PARAMETER P(T) IN SOME QUASI-LINEAR PARABOLIC DIFFERENTIAL-EQUATIONS
CANNON, JR
LIN, YP
[J]. INVERSE PROBLEMS, 1988, 4 (01) : 35 - 45
[8] Parallel techniques for a boundary value problem with non-classic boundary conditions
Dehghan, M
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2003, 137 (2-3) : 399 - 412
[9] Finding a control parameter in one-dimensional parabolic equations
Dehghan, M
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2003, 135 (2-3) : 491 - 503
[10] Identification of parameters in semilinear parabolic equations
Liu, XH
[J]. ACTA MATHEMATICA SCIENTIA, 1999, 19 (02) : 175 - 180

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