A continuing exploration of a decomposed compact method for highly oscillatory wave problems

This paper concerns a highly effective and decomposed compact scheme for solving a highly oscillatory paraxial Helmholtz problem in radially symmetric fields. The decomposition is utilized in the transverse direction to eliminate the singularity of the differential equation in polar coordinates. Numerical stability of the splitting scheme is investigated. It is shown that the numerical method introduced is not only highly accurate and efficient due to its straightforward algorithmic structure, but also stable under reasonable constraints for practical applications. Computational examples are presented to illustrate our conclusions.