Abstract
Numerical ordinary-differential-equation (ODE) methods have been shown to have distinct advantages for solving parabolic wave equations. In this presentation, we describe how to apply ODE approaches to handle arbitrary boundaries and boundary conditions associated with parabolic wave equations. A procedure has been developed to handle general boundary conditions and to advance the solution in a nonrectangular region all by ODE methods and plane trigonometry. Application of ODE methods is aiming at range-dependent problems; since these methods are quite general purpose, the range-independent cases are automatically accommodated. The effectiveness of ODE applications will be shown by a problem with irregular bottom and Neumann bottom boundary condition.
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