On the method of lines for a non-linear heat equation with functional dependence

1998 ◽  
Vol 69 (1) ◽  
pp. 61-74 ◽  
Author(s):  
H. Leszczyński
Keyword(s):  
Heat Equation ◽  
Functional Dependence ◽  
Method Of Lines ◽  
Linear Heat Equation ◽  
Linear Heat ◽  
The Method Of Lines ◽  
Non Linear

scholarly journals On the Construction of Solutions to a Problem with a Free Boundary for the Non-linear Heat Equation

2020 ◽  
pp. 694-707
Author(s):  
Alexander L. Kazakov ◽  
Lev F. Spevak ◽  
Ming-Gong Lee
Keyword(s):  
Cauchy Problem ◽  
Free Boundary ◽  
Heat Equation ◽  
Exact Solutions ◽  
Heat Wave ◽  
Wave Type ◽  
Linear Heat Equation ◽  
Linear Heat ◽  
Non Linear ◽  
The Cauchy Problem

The construction of solutions to the problem with a free boundary for the non-linear heat equation which have the heat wave type is considered in the paper. The feature of such solutions is that the degeneration occurs on the front of the heat wave which separates the domain of positive values of the unknown function and the cold (zero) background. A numerical algorithm based on the boundary element method is proposed. Since it is difficult to prove the convergence of the algorithm due to the non-linearity of the problem and the presence of degeneracy the comparison with exact solutions is used to verify numerical results. The construction of exact solutions is reduced to integrating the Cauchy problem for ODE. A qualitative analysis of the exact solutions is carried out. Several computational experiments were performed to verify the proposed method

scholarly journals On a non-homogeneous and non-linear heat equation

2015 ◽  
Vol 12 (4) ◽  
pp. 289-320
Author(s):  
Luca Bisconti ◽  
Matteo Franca
Keyword(s):  
Heat Equation ◽  
Linear Heat Equation ◽  
Linear Heat ◽  
Non Linear
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