Stability Analysis Of Marching Method

Stability and convergence are the mainly standards to the numerical solutions of differential equation. Marching method based on Dirichlet-to-Neumann map is widely used to compute the wave propagration in acoustic waveguide. Its convergence have been proved. But there is little study on its stability. This paper is mainly study its stability.During the process ,we have to compute inverse of matrix ((?)+i(?)).But thematrix may become ill-conditioned. When step numbers along marching direction is too large or discreteness along the depth direction unreasonably, the marching method will be not numerically stable.Two methods are given to improve the ill-conditioned matrix ((?)+i(?)).Thefirst method is discretize the depth direction averagely. If this method disabled. The equilibrium method is introduced to improve the condition numbers under the average discreteness.The result indicated that, the proposed method is highly effective ,stable, and we can get the real wave propagation.