When studying stationary and wave processes of different physical nature (oscillations, heat-conductivity, diffusion, etc), we often come to Laplace and Helmholtz equations:

In electrodynamics, U represents the electric field potential, created by charges or currents provided that there are not volume charges in the region. To illustrate the application of the generalized Fourier method of variable separation (GFM), we consider the internal hybrid boundary problem for these equations in rectangular domain on the plane. The geometry of the task is depicted in Fig. 1…