Stable Explicit Scheme for the Ocean Acoustic Wave Equation

摘要

A class of ocean acoustic wave propagation problems is represented by a parabolic equation of the Schrodinger type. Using conventional explicit finite difference schemes, e.g., the Euler scheme, to solve the parabolic wave equation is unstable. Thus, important advantages of explicit schemes are completely missing. This paper presents a conditionally stable explicit scheme by introducing an extra dissipatative term. This new explicit scheme is then applied to solve the ocean acoustic parabolic wave equation fully utilizing the advantage of explicit schemes. The theoretical development, the c cheme to a realistic ocean acoustic problem is included. The solution obtained is compared with the unconditionally stable Crank-Nicolson solution. (Author)