The use of Chebyshev cardinal functions for the solution of a partial differential equation with an unknown time-dependent coefficient subject to an extra measurement

A numerical technique is presented for the solution of a parabolic partial differential equation with a time-dependent coefficient subject to an extra measurement. The method is derived by expanding the required approximate solution as the elements of Chebyshev cardinal functions. Using the operatio...

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Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 235; no. 3; pp. 669 - 678
Main Authors: Lakestani, Mehrdad, Dehghan, Mehdi
Format: Journal Article
Language:English
Published: Kidlington Elsevier B.V 01.12.2010
Elsevier
Subjects:
Algebra
Approximation
Chebyshev approximation
Chebyshev cardinal functions
Coefficients
Computation
Derivatives
Exact sciences and technology
Mathematical analysis
Mathematical models
Mathematics
Numerical analysis
Numerical analysis in abstract spaces
Numerical analysis. Scientific computation
Operational matrix of derivative
Parabolic inverse problem
Parameter determination problem
Partial differential equations
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Unknown diffusion coefficient
Operational matrix of derivative
Parabolic inverse problem
Parameter determination problem
Chebyshev cardinal functions
Unknown diffusion coefficient
Initial value problem
Partial differential equation
Inverse problem
Parabolic equation
Numerical analysis
Boundary value problem
Applied mathematics
Algebraic equation
ISSN:0377-0427, 1879-1778
Online Access:Get full text
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Description
Summary:A numerical technique is presented for the solution of a parabolic partial differential equation with a time-dependent coefficient subject to an extra measurement. The method is derived by expanding the required approximate solution as the elements of Chebyshev cardinal functions. Using the operational matrix of derivative, the problem can be reduced to a set of algebraic equations. From the computational point of view, the solution obtained by this method is in excellent agreement with those obtained by previous works and also it is efficient to use.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2010.06.020