ASA 125th Meeting Ottawa 1993 May

5pUW3. Prufer transforms and numerical solutions to the Helmholtz equation.

Arthur B. Baggeroer

MIT, Rm. 5-204, Cambridge, MA 02139

The Prufer transformation maps the second-order, linear Helmholtz differential equation to two first-order, nonlinear differential equations. The coupling between the two separates such that the equation for the eigenvalue is a single nonlinear first-order equation. This transformation has long been useful in theoretical studies of Strum--Liouville where many properties of the eigenvalues have been derived using it. It turns out also to have some useful numerical properties especially for problems involving waveguides where the coupling between the boundaries is poorly conditioned. It also identifies explicitly the both stability points in the evanescent sections of the modes and the local oscillation frequency in the ducted section. The numerical aspects of using the Prufer transform and some examples are discussed in the presentation.