A higher-order energy-conserving parabolic equation for range dependent ocean depth, sound speed, and density

Outgoing solutions of the wave equation, including parabolic equation (PE) and normal-mode solutions, are usually formulated so that pressure is continuous with range for range-dependent problems. The approach of conserving energy is applied to derive a higher-order energy-conserving PE that provides improved accuracy for problems involving large ocean bottom slopes and large range and depth variations in sound speed and density. A special numerical approach and complex Pade coefficients are applied to suppress Gibbs' oscillations. The back-propagated half-space field, an improved PE starter, is applied to handle wide propagation angles. Reference solutions generated with a complex ray model and with the rotated PE are used for comparison.