THE LAGRANGE PADE PARABOLIC EQUATION (LP-PE) FOR THE PREDICTION OF LONG-RANGE SOUND-PROPAGATION IN THE ATMOSPHERE

A new formulation of the parabolic equation (PE) method for the soluti on of the two-dimensional sound wave propagation in realistic atmosphe res is derived, The new PE simultaneously reduces the errors implicit in the parabolic approximation and those due to finite step sizes in t he range variable, thereby allowing large range steps to be used leadi ng to much higher computational speeds than the standard Crank-Nichols on (CN) method. The new algorithm is based on an expansion of implicit functions due to Lagrange and can be interpreted as a sequence of CN- like steps with varying parameters. Copyright (C) 1996 Elsevier Scienc e Ltd