The iterative transformation method: numerical solution of one-dimensional parabolic moving boundary problems

2001 ◽  
Vol 78 (2) ◽  
pp. 213-223 ◽  
Author(s):  
Riccardo Fazio
Keyword(s):  
Numerical Solution ◽  
Moving Boundary ◽  
Transformation Method ◽  
Moving Boundary Problems ◽  
Boundary Problems ◽  
One Dimensional

A Four-Step Fixed-Grid Method for 1D Stefan Problems

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
M. Tadi
Keyword(s):  
Free Boundary ◽  
Moving Boundary ◽  
Free Boundary Problems ◽  
Grid Method ◽  
Moving Boundary Problems ◽  
Boundary Problems ◽  
One Dimensional ◽  
Nonlinear Part ◽  
Stefan Problems ◽  
Fixed Grid

This note is concerned with a fixed-grid finite difference method for the solution of one-dimensional free boundary problems. The method solves for the field variables and the location of the boundary in separate steps. As a result of this decoupling, the nonlinear part of the algorithm involves only a scalar unknown, which is the location of the moving boundary. A number of examples are used to study the applicability of the method. The method is particularly useful for moving boundary problems with various conditions at the front.

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