On shooting methods for the discrete Helmholtz equation with constant coefficients

Summary The paper is concerned with shooting solvers for the Helmholtz equation with constant coefficients in two dimensions using finite differences for the discretization. Dirichlet boundary conditions are treated though other conditions are possible. Beginning with a single shooting method some recursive multiple shooting methods are developed. It will be shown that the performance of the algorithms may be improved considerably by a redundance-free recursion. The number of operations required for one solution will be computed, but without preparing some matrices which do not depend on the boundary conditions and the inhomogenity. For a square withn×n points the number is of the orderO(n ²⁺⁽ⁿ⁾) with . The method will be compared with a multi-grid program and finally — as an example—a Stokes-solver and some numerical results with the shooting method are given.