An Expucit Finite-difference Scheme for Solving the Ocean Acoustic Parabouc Wave Equation

Many different numerical models exist for solving the parabolic wave equation. Hardin and Tappert[2] suggested a split-step algorithm in conjunction with the fast Fourier Transform (FFr) method. Lee and Papadakis[3] used a scheme which is based on the predictor-corrector technique of Adams-Bashforth; Lee, Botseas and Papadakis[4] introduced an implicit finitedifference scheme. Chan, Shen and Lee[S] developed an explicit scheme where the instability intrinsic in the forward difference scheme is removed by an additional diffusive term which is not in the original formulation of the physical problem. A review of difference schemes applied to the equation of Schrodinger type is presented by Chan and Shen[6]. This also included schemes derived by splitting the original complex equation into a real system. We propose a second order explicit scheme on a staggered grid where the real and imaginary part of the function are leap-frogged in the variable r and centered differenced in the variable z. Analysis and tests of the stability condition and of the accuracy of me scheme are presented in Sec~. 2 and 3, respectively. The last section summarized in this study.