scholarly journals Approximate Solution of Inverse Problem for Elliptic Equation with Overdetermination

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Charyyar Ashyralyyev ◽  
Mutlu Dedeturk
Keyword(s):  
Inverse Problem ◽  
Approximate Solution ◽  
Elliptic Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Stability Estimates ◽  
Two Dimensional ◽  
Accuracy Difference ◽  
Coercive Stability

A…finite difference method for the approximate solution of the inverse problem for the multidimensional elliptic equation with overdetermination is applied. Stability and coercive stability estimates of the fi…rst and second orders of accuracy difference schemes for this problem are established. The algorithm for approximate solution is tested in a two-dimensional inverse problem.

scholarly journals Finite Difference Method for the Reverse Parabolic Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Charyyar Ashyralyyev ◽  
Ayfer Dural ◽  
Yasar Sozen
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Parabolic Problem ◽  
Dirichlet Condition ◽  
Parabolic Differential Equation ◽  
Stability Estimates ◽  
Accuracy Difference ◽  
Multipoint Boundary Condition ◽  
Coercive Stability

A finite difference method for the approximate solution of the reverse multidimensional parabolic differential equation with a multipoint boundary condition and Dirichlet condition is applied. Stability, almost coercive stability, and coercive stability estimates for the solution of the first and second orders of accuracy difference schemes are obtained. The theoretical statements are supported by the numerical example.

scholarly journals Solving of Two-Dimensional Unsteady-State Heat-Transfer Inverse Problem Using Finite Difference Method and Model Prediction Control Method

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Shoubin Wang ◽  
Rui Ni
Keyword(s):  
Heat Transfer ◽  
Inverse Problem ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Measurement Errors ◽  
Control Method ◽  
Two Dimensional ◽  
Measurement Point ◽  
Prediction Control

The Inverse Heat Conduction Problem (IHCP) refers to the inversion of the internal characteristics or thermal boundary conditions of a heat transfer system by using other known conditions of the system and according to some information that the system can observe. It has been extensively applied in the fields of engineering related to heat-transfer measurement, such as the aerospace, atomic energy technology, mechanical engineering, and metallurgy. The paper adopts Finite Difference Method (FDM) and Model Predictive Control Method (MPCM) to study the inverse problem in the third-type boundary heat-transfer coefficient involved in the two-dimensional unsteady heat conduction system. The residual principle is introduced to estimate the optimized regularization parameter in the model prediction control method, thereby obtaining a more precise inversion result. Finite difference method (FDM) is adopted for direct problem to calculate the temperature value in various time quanta of needed discrete point as well as the temperature field verification by time quantum, while inverse problem discusses the impact of different measurement errors and measurement point positions on the inverse result. As demonstrated by empirical analysis, the proposed method remains highly precise despite the presence of measurement errors or the close distance of measurement point position from the boundary angular point angle.

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