Numerical solution of the inverse problem of determining an unknown source term in a two-dimensional heat equation

2004 ◽  
Vol 152 (3) ◽  
pp. 659-666 ◽  
Author(s):  
Afet Golayoglu Fatullayev
Keyword(s):  
Inverse Problem ◽  
Heat Equation ◽  
Numerical Solution ◽  
Source Term ◽  
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.

The Best Perturbation Method for the Parameter Inversion of Two-Dimension Convection-Diffusion Equation

2013 ◽  
Vol 380-384 ◽  
pp. 1143-1146
Author(s):  
Xiang Guo Liu
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Perturbation Method ◽  
Numerical Simulations ◽  
Numerical Solution ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Parameter Inversion ◽  
Parametric Inversion

The paper researches the parametric inversion of the two-dimensional convection-diffusion equation by means of best perturbation method, draw a Numerical Solution for such inverse problem. It is shown by numerical simulations that the method is feasible and effective.

scholarly journals A Two Dimensional Discrete Mollification Operator and the Numerical Solution of an Inverse Source Problem

Axioms ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 89 ◽  
Author(s):  
Manuel Echeverry ◽  
Carlos Mejía
Keyword(s):  
Inverse Problem ◽  
Source Term ◽  
Fractional Diffusion ◽  
Inverse Source Problem ◽  
Two Dimensional ◽  
Regularization Procedure ◽  
Numerical Examples ◽  
Convergence Results ◽  
Time Fractional Diffusion Equation ◽  
Operator Convergence

We consider a two-dimensional time fractional diffusion equation and address the important inverse problem consisting of the identification of an ingredient in the source term. The fractional derivative is in the sense of Caputo. The necessary regularization procedure is provided by a two-dimensional discrete mollification operator. Convergence results and illustrative numerical examples are included.

scholarly journals Identification of spacewise dependent right-hand side in two dimensional parabolic equation

2021 ◽  
Vol 2092 (1) ◽  
pp. 012019
Author(s):  
LingDe Su ◽  
V. I. Vasil’ev
Keyword(s):  
Inverse Problem ◽  
Parabolic Equation ◽  
Numerical Solution ◽  
Hand Function ◽  
Adjoint Operator ◽  
Two Dimensional ◽  
Right Hand ◽  
Final Time Point ◽  
The Right ◽  
Constructed Self

Abstract In this paper numerical solution of the inverse problem of determining a spacewise dependent right-hand side function in two dimensional parabolic equation is considered. Usually, the right-hand side function dependent on spatial variable is obtained from measured data of the solution at the final time point. Many mathematical modeling problems in the field of physics and engineering will encounter the inverse problems to identify the right-hand terms. When studying an inverse problem of identifying the spacewise dependent right-hand function, iterative methods are often used. We propose a new conjugate gradient method based on the constructed self-adjoint operator of the equation for numerical solution of the function and numerical examples illustrate the efficiency and accuracy.

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