The generalized method of lines based on the discretization technique of the pseudospectral method

Abstract

In this paper, a novel semianalytical higher order numerical approach to solve electromagnetic field boundary value problems is described. This pseudospectral-based method of lines is developed by combining the pseudospectral technique and the method of lines so that it not only has a high accuracy of the semianalytical technique in the line direction, but also maintains high accuracy in the discrete direction. The pseudospectral-based discretization technique, distribution of collocation nodes, global interpolation of the differential quadrature, second-order difference matrix for various homogeneous boundary conditions, and decoupling of coupled ordinary differential equations are discussed in detail. Our numerical results demonstrate that this higher order semianalytical method can efficiently solve the boundary value problems with fewer mesh lines when compared to the conventional method of lines. It primarily shows that this method will be a competitive technique to model time-harmonic complex electromagnetic problems. ©1999 John Wiley & Sons, Inc. Microwave Opt Technol Lett 20: 339–342, 1999.