The method of lines to reconstruct a moving boundary for a one-dimensional heat equation in a multilayer domain

2010 ◽  
Vol 71 (2) ◽  
pp. 157-170 ◽  
Author(s):  
Ji-Chuan Liu ◽  
Ting Wei
Keyword(s):  
Heat Equation ◽  
Moving Boundary ◽  
Method Of Lines ◽  
One Dimensional ◽  
The Method Of Lines

scholarly journals Method of lines for solving linear equations of mathematical physics with the third and first types boundary conditions

2021 ◽  
Vol 2131 (3) ◽  
pp. 032041
Author(s):  
M Kh Eshmurodov ◽  
K M Shaimov ◽  
I Khujaev ◽  
J Khujaev
Keyword(s):  
Boundary Conditions ◽  
Characteristic Equation ◽  
Transition Matrix ◽  
Method Of Lines ◽  
Mathematical Physics ◽  
Sweep Method ◽  
Discontinuous Solutions ◽  
One Dimensional ◽  
The Third ◽  
The Method Of Lines

Abstract The use of the method of lines in solving multidimensional problems of mathematical physics makes it possible to eliminate the discrepancies caused by the use of the sweep method in certain coordinates. As a result, the solution of the Poisson equation, for example, is obtained without using the relaxation method. In the article, the problem on the eigenvalues and vectors of the transition matrix is solved for boundary conditions of the third and first types, used to solve a one-dimensional equation of parabolic type by the method of lines. Due to the features of boundary conditions of the third type for determining the eigenvalues, a mixed method was proposed based on the Vieta theorem and the representation of the characteristic equation in trigonometric form typical for the method of lines. To solve the eigenvector problem, a simple sweep method was used with the algebraic compliments to the transition matrix. Discontinuous solutions of a one-dimensional parabolic equation were presented for various values of complex 1 -αl; the method for solving the characteristic equation was selected based on these values. The calculation results are in good agreement with the analytical solution.

scholarly journals An efficient numerical method for one-dimensional hyperbolic interface problems

2019 ◽  
Vol 29 ◽  
pp. 01002
Author(s):  
Chartese Jones ◽  
Xu Zhang
Keyword(s):  
Finite Element ◽  
Numerical Experiments ◽  
Numerical Scheme ◽  
Method Of Lines ◽  
Interface Problems ◽  
Uniform Mesh ◽  
One Dimensional ◽  
Immersed Finite Element ◽  
New Methods ◽  
The Method Of Lines

In this paper, we develop an efficient numerical scheme for solving one-dimensional hyperbolic interface problems. The immersed finite element (IFE) method is used for spatial discretization, which allows the solution mesh to be independent of the interface. Consequently, a fixed uniform mesh can be used throughout the entire simulation. The method of lines is used for temporal discretization. Numerical experiments are provided to show the features of these new methods.

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