Boundary Integral Solutions of the Heat Equation

Boundary temperature reconstruction in an inverse heat conduction problem using boundary integral equation method

‎In this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎To this end‎, ‎the boundary integral equation method is used‎. ‎Since the resulting system of linea...

The Boundary Integral Equation Method

boundary temperature reconstruction in an inverse heat conduction problem using boundary integral equation method

‎in this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎this problem consists of determining the temperature on the interior boundary curve from the cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎to this end‎, ‎the boundary integral equation method is used‎. ‎since the resulting system of linea...

‎Solving Some Initial-Boundary Value Problems Including Non-classical ‎C‎ases of Heat Equation By Spectral and Countour Integral ‎Methods‎

In this paper, we consider some initial-boundary value problems which contain one-dimensional heat equation in non-classical case. For this problem, we can not use the classical methods such as Fourier, Laplace transformation and Fourier-Birkhoff methods. Because the eigenvalues of their spectral problems are not strictly and they are repeated or we have no eigenvalue. The presentation of the s...

Boundary Integral Equations of the First Kind for the Heat Equation

Boundary element methods are being applied with increasing frequency to time dependent problems, especially to boundary value problems for parabolic differential equations. Here we shall consider the heat equation as the prototype of such equations. Various types of integral equations arise when solving boundary value problems for the heat equation. An important one is the single layer heat pot...