The Sinc-Galerkin method for solving an inverse parabolic problem with unknown source term

2012 ◽  
Vol 29 (1) ◽  
pp. 64-78 ◽  
Author(s):  
A. Shidfar ◽  
A. Babaei
Keyword(s):  
Galerkin Method ◽  
Parabolic Problem ◽  
Source Term ◽  
Unknown Source ◽  
Inverse Parabolic Problem

scholarly journals Numerical method of identification of an unknown source term in a heat equation

2002 ◽  
Vol 8 (2) ◽  
pp. 161-168 ◽  
Author(s):  
Afet Golayoğlu Fatullayev
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Numerical Method ◽  
Minimization Problem ◽  
Unknown Function ◽  
Source Term ◽  
Numerical Procedure ◽  
Numerical Examples ◽  
Unknown Source

A numerical procedure for an inverse problem of identification of an unknown source in a heat equation is presented. Approach of proposed method is to approximate unknown function by polygons linear pieces which are determined consecutively from the solution of minimization problem based on the overspecified data. Numerical examples are presented.

Identifying an unknown source term in radial heat conduction

2012 ◽  
Vol 20 (3) ◽  
pp. 335-349 ◽  
Author(s):  
Wei Cheng ◽  
Yun-Jie Ma ◽  
Chu-Li Fu
Keyword(s):  
Heat Conduction ◽  
Source Term ◽  
Unknown Source ◽  
Radial Heat

scholarly journals Wavelet-Galerkin Method for Identifying an Unknown Source Term in a Heat Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Fangfang Dou
Keyword(s):  
Heat Equation ◽  
Galerkin Method ◽  
Identification Problem ◽  
Stability And Convergence ◽  
Wavelet Galerkin Method ◽  
Unknown Source ◽  
Frequency Components ◽  
Ill Posed ◽  
Meyer Wavelets ◽  
The Stability

We consider the problem of identification of the unknown source in a heat equation. The problem is ill posed in the sense that the solution (if it exists) does not depend continuously on the data. Meyer wavelets have the property that their Fourier transform has compact support. Therefore, by expanding the data and the solution in the basis of the Meyer wavelets, high-frequency components can be filtered away. Under the additional assumptions concerning the smoothness of the solution, we discuss the stability and convergence of a wavelet-Galerkin method for the source identification problem. Numerical examples are presented to verify the efficiency and accuracy of the method.

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