It is extremely complicated and impractical to develop a tool which can solve all acoustics problems in one model. The cost of this effort is very expensive both in labor and in time. A practical approach is to solve a class of acoustics problems efficiently and then extends the solution to solve a more general class of problems. A class of acoustic propagation problems involves long-range, low-frequency under range-dependent environments in fluid medium drew interest of acoustic scientists and engineers. It is desirable to have a model which can efficiently solve the above class of problems. To attack this class of problems, Frederick Tappert introduced the Parabolic Equation Approximation Method. This paper reviews what contributions Tappert has made for the formulation of the representative Parabolic Equation (PE), then, the Split-step Fourier algorithm to solve the PE. The introduction of the PE not only can it solve the above class of problems effectively but also influence the progress of developing numerious models to a variety of realistic problems in the acoustics community. This paper is confined to state Tappert's contribution in the PE development to the acoustics community. A description of the original development of the PE approximation is outlined along with the solution by the Split-step Fourier algorithm. Then, the vital influence of the PE approximation to the acoustics community is discussed.
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