Marching schemes for Cauchy wave propagation problems in laterally varying waveguides

This paper intends to develop practical marching schemes for Cauchy problems of the Helmholtz equation in laterally varying waveguides. We arrive at a stable representation of the marching solutions in waveguides. Based on the representation, a second-order marching scheme is then constructed to eliminate the ill-conditioning and compute the wave propagation in wave guides with laterally variable mediums. In the end, extensive experiments are implemented to verify the efficiency and accuracy of the marching scheme in various waveguides, and we also point out the application scope of the scheme.