RATIONAL SQUARE-ROOT APPROXIMATIONS FOR PARABOLIC EQUATION ALGORITHMS

In this article, stable Pade approximations to the function root 1+z a re derived by choosing a branch cut in the negative half-plane. The Pa de coefficients are complex and may be derived analytically to arbitra ry order from the corresponding real coefficients associated with the principal branch defined by z< -1, T(z) = 0 [T(z) denotes the imaginar y part of z]. The characteristics of the corresponding square-root app roximation are illustrated for various segments of the complex plane. In particular, for waveguide problems it is shown that an increasingly accurate representation may be obtained of both the evanescent part o f the mode spectrum for the acoustic case and the complex mode spectru m for the elastic case. An elastic parabolic equation algorithm is use d to illustrate the application of the new Pade approximations to a re alistic ocean environment, including elasticity in the ocean bottom. ( C) 1997 Acoustical Society of America.