Generalised method of lines for Helmholz equations by using discretisation technique of pseudospectral method

A novel semi-analytical higher-order numerical approach to solve electromagnetic field boundary-value problems is described. This pseudospectral-based method of lines is developed by combining a pseudospectral technique with the method of lines so that its solution is not only analytical along the line direction but also maintains high accuracy in the discrete direction. The pseudospectral-based discretisation strategy, distribution of collocation nodes, the global Fourier series interpolation of differential quadrature, a second-order difference matrix for various homogeneous boundary conditions, and the decoupling of coupled ordinary differential equations are all discussed in detail. Numerical results demonstrate that this pseudospectral method of lines can efficiently solve the boundary-value problems with higher accuracy when compared with the conventional method of lines. This method should be a competitive technique for modelling time-harmonic complex electromagnetic problems