scholarly journals Analytical and numerical solution of the heat conduction problem in the rod

2017 ◽  
Vol 16 (4) ◽  
pp. 79-86
Author(s):  
Ewa Węgrzyn-Skrzypczak ◽  
Tomasz Skrzypczak
Keyword(s):  
Heat Conduction ◽  
Numerical Solution ◽  
Heat Conduction Problem

Numerical solution of two-dimensional radially symmetric inverse heat conduction problem

2015 ◽  
Vol 23 (2) ◽  
Author(s):  
Zhi Qian ◽  
Benny Y. C. Hon ◽  
Xiang Tuan Xiong
Keyword(s):  
Heat Conduction ◽  
Numerical Solution ◽  
Heat Conduction Problem ◽  
Inverse Heat Conduction Problem ◽  
Stability And Convergence ◽  
Two Dimensional ◽  
Inverse Heat Conduction ◽  
Convergence Error ◽  
Regularization Techniques ◽  
Ill Posed

AbstractWe investigate a two-dimensional radially symmetric inverse heat conduction problem, which is ill-posed in the sense that the solution does not depend continuously on input data. By generalizing the idea of kernel approximation, we devise a modified kernel in the frequency domain to reconstruct a numerical solution for the inverse heat conduction problem from the given noisy data. For the stability of the numerical approximation, we develop seven regularization techniques with some stability and convergence error estimates to reconstruct the unknown solution. Numerical experiments illustrate that the proposed numerical algorithm with regularization techniques provides a feasible and effective approximation to the solution of the inverse and ill-posed problem.

scholarly journals Local fractional Euler’s method for the steady heat-conduction problem

2016 ◽  
Vol 20 (suppl. 3) ◽  
pp. 735-738 ◽  
Author(s):  
Feng Gao ◽  
Xiao-Jun Yang
Keyword(s):  
Heat Conduction ◽  
Exact Solutions ◽  
Numerical Solution ◽  
Heat Conduction Problem ◽  
Relaxation Equation ◽  
Euler’S Method ◽  
Steady Heat Conduction ◽  
First Time ◽  
Steady Heat

In this paper, the local fractional Euler?s method is proposed to consider the steady heat-conduction problem for the first time. The numerical solution for the local fractional heat-relaxation equation is presented. The comparison between numerical and exact solutions is discussed.

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