The Cayley transform and boundary integral equations to an initial boundary value problem for the heat equation

A numerical solution of the initial boundary value problem for the heat equation has a great significance as regards the number of applications in engineering sciences. This problem arises also at the solution of the inverse boundary value problems in thermal tomography. The approximate solution can be found with the boundary integral equations method which may be used in the diverse variants. We combine the Cayley transform and the boundary integral equations for the numerical solution of the interior initial boundary value problem for the heat equation.