Rothe's Method for the Heat Equation and Boundary Integral Equations

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 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...

CAS WAVELET METHOD FOR THE NUMERICAL SOLUTION OF BOUNDARY INTEGRAL EQUATIONS WITH LOGARITHMIC SINGULAR KERNELS

In this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. Themethod is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis.This approach utilizes the non-uniform Gauss-Legendre quadrature rule for ...

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...