The Selection of Basis Functions Systems for Determination of Cutoff Frequency of Waveguides and Resonators of Complex Shape with the Help of R-functions Method

The work focuses on the problem of determination of cutoff frequency of waveguides and resonators of a complex shape. The problem is sold by method of R-functions. This approach has a lot of advantages, it possesses geometric flexibility, broad capabilities of numerical realization as for the production of the variation problem and for the selection of basis functions system as well. As basis functions the polynomials (trigonometrical, power, Tchebyshev of I and II types, Legendre, Gegenbauer) or local functions (atomic functions, splines) are used. The contrastive analysis of approximate boundary value problem solving is carried out in accordance to the basis functions system selected.