A numerical method for solving a nonlinear inverse parabolic problem

Pourgholi, Reza; Rostamian, M.; Emamjome, M.

doi:10.1080/17415977.2010.518287

Cited by 29 publications

(8 citation statements)

References 10 publications

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“…Various problems for equations of this type were investigated and many results have been obtained in di¤erent ways. The practical advantages of remote sensing are what make the inverse problems important in [4,6,11] .The FOURIER M ETHOD EULER-BERNOULLI BEAM EQ UATION 515 investigation of various problems concerning 4 th order homogeneous, linear and quasi-linear equations has been one of the most attractive areas for mathematicians and engineers due to their importance in the solution of several engineering problems. The reader is refereed to [9,10,12] for some relevant previous work on linear and quasi-linear equations, applications.…”

Section: Introductionmentioning

confidence: 99%

Fourier Method for Inverse Coefficient Euler-Bernoulli Beam Equation

Bağlan¹

2018

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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Section: Introductionmentioning

confidence: 99%

Fourier Method for Inverse Coefficient Euler-Bernoulli Beam Equation

Bağlan¹

2018

Communications Faculty of Science University of Ankara Series A1Mathematics and Statistics

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“…Crank–Nicolson scheme is used for the finite difference method. In , numerical solution of the inverse coefficient problems for nonlinear parabolic equation is considered, and the backward finite difference method and regularization method are used for ill‐posedness of the problem. In , Crank–Nicolson scheme is considered for numerical solution.…”

Section: Introductionmentioning

confidence: 99%

An inverse coefficient problem for a quasilinear parabolic equation with periodic boundary and integral overdetermination condition

Bağlan

Kanca

2014

Math Methods in App Sciences

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In this paper, the inverse problem of finding the time‐dependent coefficient of heat capacity together with the solution periodic boundary and integral overdetermination conditions is considered. Under some natural regularity and consistency conditions on the input data, the existence, uniqueness, and continuous dependence upon the data of the solution are shown. Some considerations on the numerical solution for this inverse problem are presented with an example. Copyright © 2014 John Wiley & Sons, Ltd.

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“…A solution was proposed to investigate inverse problem by using a finite difference method and a least square method in literature [4]. Some other methods, such as the method of fundamental solutions [5], were also used to solve this kind of inverse heat conduction problem.…”

Section: Introductionmentioning

confidence: 99%

Application of the RBF Method to the Estimation of Temperature on the External Surface in Laminar Pipe Flow

Lyu

Zhang

2013

Mathematical Problems in Engineering

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The inverse heat conduction problem on the heat transfer characteristics of cooled/heated laminar flows through finite length thick-walled circular tubes is studied, using temperature measurements taken at several different locations within the fluid in this paper. The method of radial basis functions is coupled with the boundary control technique to estimate the unknown temperature on the external surface of the circular pipe. The main idea of the proposed method is to solve the direct problem instead of solving the inverse problem directly. The temperature data obtained from the direct problem are used to simulate the temperature measurement for the inverse problem, and during the calculation, the Tikhonov regularization and L-curve methods are employed to solve the inverse problem. Therefore, this study also considers the influence of errors in these measurements upon the precision of the estimated results as well as the influence of the locations and number of sensors used upon the accuracy of the estimated results. The results indicate that the accuracy of the estimated results is improved by taking temperature measurements in locations close to the the unknown boundary. Finally, the results confirm that the proposed method is capable of yielding accurate results even when errors in the temperature measurements are present.

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A numerical method for solving a nonlinear inverse parabolic problem

Cited by 29 publications

References 10 publications

Fourier Method for Inverse Coefficient Euler-Bernoulli Beam Equation

Fourier Method for Inverse Coefficient Euler-Bernoulli Beam Equation

An inverse coefficient problem for a quasilinear parabolic equation with periodic boundary and integral overdetermination condition

Application of the RBF Method to the Estimation of Temperature on the External Surface in Laminar Pipe Flow

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