A difference scheme for a conjugate-operator model of the heat conduction problem on non-matching grids

2016 ◽  
Keyword(s):  
Heat Conduction ◽  
Difference Scheme ◽  
Heat Conduction Problem ◽  
Conjugate Operator ◽  
Operator Model

scholarly journals METHOD OF LINES AND FINITE DIFFERENCE SCHEMES WITH THE EXACT SPECTRUM FOR SOLUTION THE HYPERBOLIC HEAT CONDUCTION EQUATION

2011 ◽  
Vol 16 (1) ◽  
pp. 220-232 ◽  
Author(s):  
Harijs Kalis ◽  
Andris Buikis
Keyword(s):  
Heat Conduction ◽  
Finite Difference ◽  
Difference Scheme ◽  
Heat Conduction Equation ◽  
Heat Conduction Problem ◽  
Method Of Lines ◽  
Numerical Results ◽  
Conduction Equation ◽  
Finite Difference Schemes ◽  
Hyperbolic Heat Conduction

This paper is concerning with the 1-D initial–boundary value problem for the hyperbolic heat conduction equation. Numerical solutions are obtained using two discretizations methods – the finite difference scheme (FDS) and the difference scheme with the exact spectrum (FDSES). Hyperbolic heat conduction problem with boundary conditions of the third kind is solved by the spectral method. Method of lines and the Fourier method are considered for the time discretization. Finite difference schemes with central difference and exact spectrum are analyzed. A novel method for solving the discrete spectral problem is used. Special matrix with orthonormal eigenvectors is formed. Numerical results are obtained for steel quenching problem in the plate and in the sphere with holes. The hyperbolic heat conduction problem in the sphere with holes is reduced to the problem in the plate. Some examples and numerical results for two typical problems related to hyperbolic heat conduction equation are presented.

scholarly journals Stable difference scheme for a nonlocal boundary value heat conduction problem

2018 ◽  
Vol 1 (1) ◽  
pp. 1-10
Author(s):  
Makhmud A. Sadybekov
Keyword(s):  
Heat Conduction ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Heat Equation ◽  
Difference Scheme ◽  
Difference Method ◽  
Heat Conduction Problem ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Strong Regularity

AbstractIn this paper, a new finite difference method to solve nonlocal boundary value problems for the heat equation is proposed. The most important feature of these problems is the non-self-adjointness. Because of the non-self-adjointness, major difficulties occur when applying analytical and numerical solution techniques. Moreover, problems with boundary conditions that do not possess strong regularity are less studied. The scope of the present paper is to justify possibility of building a stable difference scheme with weights for mentioned type of problems above.

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