Functional Approximations for Solving Boundary Value Problems by Computer

The use of functional (as opposed to numerical) approximations in solving electromagnetic boundary value problems is presented. Galerkin´s method is modified to simplify the choice of trial functions by permitting use of trial functions which do not satisfy certain boundary conditions. A test problem, the dielectric loaded rectangular waveguide, is worked using both the modified and unmodified Galerkin´s method with identical results. This method is then applied to the arbitrary waveguide. The cutoff frequencies and computer drawn contour plots are presented for circular, rectangular, triangular and star-shaped waveguides.