scholarly journals Determining An Unknown Boundary Condition by An Iteration Method

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 409
Author(s):  
Dejian Huang ◽  
Yanqing Li ◽  
Donghe Pei
Keyword(s):  
Boundary Condition ◽  
Exact Solution ◽  
Heat Conduction ◽  
Iteration Method ◽  
Heat Conduction Equation ◽  
Heat Conduction Problem ◽  
Variational Iteration Method ◽  
Conduction Equation ◽  
Unknown Boundary ◽  
Initial Condition

This paper investigates the boundary value in the heat conduction problem by a variational iteration method. Applying the iteration method, a sequence of convergent functions is constructed, the limit approximates the exact solution of the heat conduction equation in a few iterations using only the initial condition. This method does not require discretization of the variables. Numerical results show that this method is quite simple and straightforward for models that are currently under research.

scholarly journals Fractal heat conduction problem solved by local fractional variation iteration method

2013 ◽  
Vol 17 (2) ◽  
pp. 625-628 ◽  
Author(s):  
Xiao-Jun Yang ◽  
Dumitru Baleanu
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Iteration Method ◽  
Heat Conduction Equation ◽  
Heat Conduction Problem ◽  
Variational Iteration Method ◽  
Conduction Equation ◽  
Variational Iteration ◽  
Fractional Heat Conduction ◽  
Variation Iteration Method

This paper points out a novel local fractional variational iteration method for processing the local fractional heat conduction equation arising in fractal heat transfer.

scholarly journals Identification of a Time-Dependent Coefficient in Heat Conduction Problem by New Iteration Method

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Dejian Huang ◽  
Yanqing Li ◽  
Donghe Pei
Keyword(s):  
Heat Conduction ◽  
Iteration Method ◽  
Heat Conduction Equation ◽  
Heat Conduction Problem ◽  
Convergent Sequence ◽  
Time Dependent ◽  
Unknown Coefficient ◽  
Initial Condition ◽  
Integral Calculus ◽  
Complex Calculation

This paper investigates the problem of identifying unknown coefficient of time dependent in heat conduction equation by new iteration method. In order to use new iteration method, we should convert the parabolic heat conductive equation into an integral equation by integral calculus and initial condition. This method constructs a convergent sequence of function, which approximates the exact solution with a few iterations and does not need complex calculation. Illustrative examples are given to demonstrate the efficiency and validity.

scholarly journals Reconstructive schemes for variational iteration method within Yang-Laplace transform with application to fractal heat conduction problem

2013 ◽  
Vol 17 (3) ◽  
pp. 715-721 ◽  
Author(s):  
Chun-Feng Liu ◽  
Shan-Shan Kong ◽  
Shu-Juan Yuan
Keyword(s):  
Heat Conduction ◽  
Laplace Transform ◽  
Fractional Derivative ◽  
Lagrange Multiplier ◽  
Iteration Method ◽  
Heat Conduction Equation ◽  
Heat Conduction Problem ◽  
Variational Iteration Method ◽  
High Accuracy ◽  
Variational Iteration

A reconstructive scheme for variational iteration method using the Yang-Laplace transform is proposed and developed with the Yang-Laplace transform. The identification of fractal Lagrange multiplier is investigated by the Yang-Laplace transform. The method is exemplified by a fractal heat conduction equation with local fractional derivative. The results developed are valid for a compact solution domain with high accuracy.

On Elliptic Inverse Heat Conduction Problems

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
M. Tadi
Keyword(s):  
Boundary Condition ◽  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Initial Guess ◽  
Unknown Boundary ◽  
Inverse Heat Conduction ◽  
Robustness To Noise ◽  
Inverse Heat Conduction Problems ◽  
New Feature

This note is concerned with a new method for the solution of an elliptic inverse heat conduction problem (IHCP). It considers an elliptic system where no information is given at part of the boundary. The method is iterative in nature. Starting with an initial guess for the missing boundary condition, the algorithm obtains corrections to the assumed value at every iteration. The updating part of the algorithm is the new feature of the present algorithm. The algorithm shows good robustness to noise and can be used to obtain a good estimate of the unknown boundary condition. A number of numerical examples are used to show the applicability of the method.

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