Inverse Problem for Two-Dimensional Heat Equation with an Unknown Source

2018 ◽  
Author(s):  
Nelya Pabyrivska ◽  
Viktor Pabyrivskyy
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Two Dimensional ◽  
Unknown Source

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.

scholarly journals A Meshless Method to Determine a Source Term in Heat Equation with Radial Basis Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Baiyu Wang ◽  
Anping Liao
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Radial Basis Functions ◽  
Meshless Method ◽  
Source Term ◽  
Initial Boundary ◽  
High Accuracy ◽  
Basis Functions ◽  
Unknown Source ◽  
Radial Basis

This paper considers a numerical method based on the radial basis functions for the inverse problem of heat equation; the inverse problem is determining an unknown source term subject to the overdetermination along with the usual initial boundary conditions, and the unknown source term is only time-dependent. The radial basis functions method is a meshless method with high accuracy for the inverse problem. Some numerical experiments using this method are presented and discussed.

scholarly journals Inverse Source Identification by the Modified Regularization Method on Poisson Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Xiao-Xiao Li ◽  
Heng Zhen Guo ◽  
Shi Min Wan ◽  
Fan Yang
Keyword(s):  
Inverse Problem ◽  
Exact Solution ◽  
Error Estimate ◽  
Poisson Equation ◽  
Source Identification ◽  
Regularization Method ◽  
Numerical Results ◽  
Two Dimensional ◽  
Internal Point ◽  
Unknown Source

This paper deals with an inverse problem for identifying an unknown source which depends only on one variable in two-dimensional Poisson equation, with the aid of an extra measurement at an internal point. Since this problem is illposed, we obtain the regularization solution by the modified regularization method. Furthermore, we obtain the Hölder-type error estimate between the regularization solution and the exact solution. The numerical results show that the proposed method is stable and the unknown source is recovered very well.

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