A direct multiple-scale approach to the parabolic equation method

A new multi-component form of the higher order parabolic approximations to the acoustic Helmholtz equation and the corresponding interface and boundary conditions are derived by the direct use of the multiple-scale approach. These new parabolic approximations have the properties of asymptotic energy conservation and asymptotic absence of the phase error. Numerical examples for some typical environments are presented.

► A new approach to the parabolic approximation is developed.
► Asymptotic energy flux conservation for our parabolic approximations is proved.
► Asymptotic absence of the phase error for our parabolic approximations is proved.
► These properties are confirmed by several numerical examples.