On a difference scheme for nonlocal heat transfer boundary-value problem

2016 ◽  
Author(s):  
Meiram E. Akhymbek ◽  
Makhmud A. Sadybekov
Keyword(s):  
Heat Transfer ◽  
Boundary Value Problem ◽  
Difference Scheme ◽  
Boundary Value

scholarly journals On Third Order Stable Difference Scheme for Hyperbolic Multipoint Nonlocal Boundary Value Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Ozgur Yildirim ◽  
Meltem Uzun
Keyword(s):  
Boundary Value Problem ◽  
Difference Scheme ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Stability Estimates ◽  
Nonlocal Boundary Value Problem ◽  
Third Order ◽  
Order Of Accuracy ◽  
Definite Operator ◽  
The Difference

This paper presents a third order of accuracy stable difference scheme for the approximate solution of multipoint nonlocal boundary value problem of the hyperbolic type in a Hilbert space with self-adjoint positive definite operator. Stability estimates for solution of the difference scheme are obtained. Some results of numerical experiments that support theoretical statements are presented.

Heat Transfer in Composite Solids with Heat Generation

1979 ◽  
Vol 101 (1) ◽  
pp. 137-143 ◽  
Author(s):  
L. Feijoo ◽  
H. T. Davis ◽  
D. Ramkrishna
Keyword(s):  
Heat Transfer ◽  
Integral Equation ◽  
Integral Operator ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Adjoint Operator ◽  
The Self ◽  
Basis Set ◽  
Inner Product ◽  
Steady State Heat Transfer

Steady-state heat transfer problems have been considered in a composite solid comprising two materials, one, a slab, which forms the bulk of the interior and the other, a plate, which forms a thin layer around the boundary. Through the use of appropriate Green’s functions, it is shown that the boundary value problem can be converted into a Fredholm integral equation of the second kind. The integral operator in the integral equation is shown to be self-adjoint under an appropriate inner product. Solutions have been obtained for the integral equation by expansion in terms of eigenfunctions of the self-adjoint integral operator, from which the solution to the boundary value problem is constructed. Two problems have been considered, for the first of which the eigenvalues and eigenvectors of the self-adjoint operator were analytically obtained; for the second, the spectral decomposition was obtained numerically by expansion in a convenient basis set. Detailed numerical computations have been made for the second problem using various types of heat source functions. The calculations are relatively easy and inexpensive for the examples considered. These examples, we believe, are sufficiently diverse to constitute a rather stringent test of the numerical merits of the eigenvalue technique used.

scholarly journals An algorithm for solving the boundary value problem of radiation heat transfer without boundary conditions for radiation intensity

2020 ◽  
pp. 114-122
Author(s):  
A.Yu. Chebotarev ◽  
◽  
P.R. Mesenev ◽  
Keyword(s):  
Heat Transfer ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Radiation Intensity ◽  
Radiation Transfer ◽  
Boundary Value ◽  
Radiation Heat Transfer ◽  
Three Dimensional ◽  
Conductive Heat ◽  
Radiation Heat

An optimization algorithm for solving the boundary value problem for the stationary equations of radiation-conductive heat transfer in the three-dimensional region is presented in the framework of the $ P_1 $ - approximation of the radiation transfer equation. The analysis of the optimal control problem that approximates the boundary value problem where they are not defined boundary conditions for radiation intensity. Theoretical analysis is illustrated by numerical examples.

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