... equations, we obtain this way, does not have non-trivial solutions. Therefore, the solution (6) not satisfy the formulated boundary problem. We can divide the surrounding contour into segments, which obviously leads to the increase in the number of boundary problems to be solved. It can be avoided by using GFM. If the function in question is represented as: (7) the equation (3) is reduced to the bilinear form: (8) At the next stage of the GFM technique, it is necessary to build the matrix of functions ...

Solving of applied problems concerning different physical processes often involves search for analytic solutions to the boundary value problems of mathematical physics. From this viewpoint, the use of the variable separation method is one of possible ways of this search. The well-studied classical Fourier method allows obtaining analytic solutions to partial differential equations satisfying a limited number of kinds of boundary conditions. The internal boundary value problems for a rectangular domain...