A refinement of the boundary element collocation method near the boundary of a two-dimensional domain using semianalytic approximation of the double layer heat potential

The solution of the first boundary-value problem for two-dimensional homogeneous equations of heat conduction with zero initial condition is studied using a collocation element of boundary elements. A semi-analytic approximation with the possibility of a double layer is proposed, which ensures uniform cubic convergence of the approximate solutions in the region. It is proved that the use of quadrature forms for approximation makes it possible to violate the uniform distribution near the border. Theoretical conclusions confirm the results of a numerical solution in a circular domain.