A new numerical approach to electromagnetics: finite-analytic method

A finite-analytic (FA) scheme, based on power series expansion, has been developed for the 2-D Helmholtz equation. The scheme developed here has proven to be better performing than the classical 5-point and 9-point finite difference (FD) schemes for the waveguide problem considered. Depending on the problem, different series expansions can be utilized for the FA scheme for higher accuracy giving the opportunity to develop a problem oriented FD scheme. Once the appropriate FA scheme has been developed one can use the resulting FD scheme to increase the accuracy and the efficiency of the solution without increasing the complexity of the FD scheme.