We introduce and analyze a collection of difference schemes for the numerical solution of a model multidimensional equation of Schrödinger type with applications to the three-dimensional parabolic wave equation arising from the sound propagation in the ocean. This collection of methods includes explicit and implicit schemes, two-level and three-level schemes and real and complex schemes. Many of these are analogous to classical schemes for the heat equation and the wave equation, but some schemes are unique to the Schrödinger equation. Von Neumann type stability results are given for all schemes. Numerical results arising from the application to an ocean acoustic problem are presented.
ASJC Scopus subject areas
- Modeling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics