Reconstruction of moving boundary for one-dimensional heat conduction equation by using the Lie-group shooting method

2012 ◽  
Vol 20 (3) ◽  
pp. 311-334 ◽  
Author(s):  
Chein-Shan Liu
Keyword(s):  
Heat Conduction ◽  
Lie Group ◽  
Heat Conduction Equation ◽  
Shooting Method ◽  
Moving Boundary ◽  
Conduction Equation ◽  
One Dimensional

The Method of Fundamental Solutions for the Moving Boundary Problem of the One-Dimension Heat Conduction Equation

2014 ◽  
Vol 1039 ◽  
pp. 59-64 ◽  
Author(s):  
Xin Jiang ◽  
Xiao Gang Wang ◽  
Yue Wei Bai ◽  
Chang Tao Pang
Keyword(s):  
Heat Conduction ◽  
Boundary Problem ◽  
Heat Conduction Equation ◽  
Moving Boundary ◽  
Numerical Solutions ◽  
Fundamental Solutions ◽  
Metal Wire ◽  
Moving Boundary Problem ◽  
Conduction Equation ◽  
Temperature Function

The melting of the material is regarded as the moving boundary problem of the heat conduction equation. In this paper, the method of fundamental solution is extended into this kind of problem. The temperature function was expressed as a linear combination of fundamental solutions which satisfied the governing equation and the initial condition. The coefficients were gained by use of boundary condition. When the metal wire was melting, process of the moving boundary was gained through the conversation of energy and the Prediction-Correlation Method. A example was given. The numerical solutions agree well with the exact solutions. In another example, numerical solutions of the temperature distribution of the metal wire were obtained while one end was heated and melting.

Truncation Error Estimates for Numerical and Analog Solutions of the Heat-Conduction Equation

1961 ◽  
Vol 83 (3) ◽  
pp. 382-383 ◽  
Author(s):  
N. H. Freed ◽  
C. J. Rallis
Keyword(s):  
Heat Conduction ◽  
Heat Flow ◽  
Finite Difference ◽  
Error Estimates ◽  
Heat Conduction Equation ◽  
Truncation Error ◽  
Mesh Size ◽  
Practical Method ◽  
Conduction Equation ◽  
One Dimensional

A practical method is presented for obtaining a meaningful estimate of the truncation error associated with fully finite-difference forms of the heat-conduction equation. The analysis is applied in this instance to the Liebmann analog equations. It may also be used with other manual and analog methods of computation, where the error due to mesh size is relatively large. An example is given deriving error estimates for a case of one-dimensional heat flow.

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