PARABOLIC EQUATION DEVELOPMENT IN THE TWENTIETH CENTURY
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Publication:2981661
DOI10.1142/S0218396X00000388zbMath1360.76264OpenAlexW4211148763MaRDI QIDQ2981661
Allan D. Pierce, Ding Lee, E. C. Shang
Publication date: 9 May 2017
Published in: Journal of Computational Acoustics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/s0218396x00000388
History of mathematics in the 20th century (01A60) Hydro- and aero-acoustics (76Q05) Research exposition (monographs, survey articles) pertaining to fluid mechanics (76-02) History of fluid mechanics (76-03)
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Cites Work
- Unnamed Item
- Current development in the numerical treatment of ocean acoustic propagation
- A parabolic approximation for elastic waves
- Bremmer series that correct parabolic approximations
- A class of nonlinear multistep a-stable numerical methods for solving stiff differential equations
- Discrete transparent boundary conditions for wide angle parabolic equations in underwater acoustics
- Reciprocity and energy theorems for waves in compressible inhomogeneous moving fluid
- A high-order numerical method for solving ocean acoustic problems
- The Harvard open ocean model: Calibration and application to dynamical process, forecasting, and data assimilation studies
- A modified wide angle parabolic wave equation
- A comparison of parabolic wave theories for linearly elastic solids
- FINITE DIFFERENCE TREATMENT OF IRREGULAR INTERFACES: AN ERROR ANALYSIS
- PARABOLIC EQUATION DEVELOPMENT IN RECENT DECADE
- A METHOD FOR THE TREATMENT OF A SLOPING SEA BOTTOM IN THE PARABOLIC APPROXIMATION
- FINITE ELEMENT METHODS FOR THE PARABOLIC EQUATION WITH INTERFACES
- Numerical Computations of Elastic Wave Equations
- The Solution of the Diffusion Equation by a High Order Correct Difference Equation
- Rays and local modes in a wedge-shaped ocean
- A wide-angle split-step algorithm for the parabolic equation
- A finite-difference treatment of interface conditions for the parabolic wave equation: The irregular interface
- Intrinsic modes in a nonseparable ocean waveguide
- A high-angle one-way wave equation for seismic wave propagation along rough and sloping interfaces
- Current and current shear effects in the parabolic approximation for underwater sound channels
- Finite-difference treatment of a time-domain parabolic equation: Theory
- A range refraction parabolic equation
- Modeling of reciprocity in the time domain using the parabolic equation method
- Extending the finite difference treatment of interfaces when using the parabolic wave equation
- A stochastic parabolic wave equation and field-moment equations for random media having spatial variation of mean refractive index
- Parabolic Wave Equation Approximations in Heterogenous Media
- Higher Order Paraxial Wave Equation Approximations in Heterogeneous Media
- A coupled 3D fluid-elastic wave propagation model: mathematical formulation and analysis
- Numerical solutions of the parabolic wave equation: An ordinary-differential-equation approach
- Finite-difference solution to the parabolic wave equation
- A finite-difference treatment of interface conditions for the parabolic wave equation: The horizontal interface
- A Parabolic Theory of Stress Wave Propagation Through Inhomogeneous Linearly Elastic Solids
- Parabolic approximations for underwater sound propagation
- Helmholtz equation as an initial value problem with application to acoustic propagation
- Relation between the solutions of the Helmhotz and parabolic equations for sound propagation
- Finite Difference Methods for the Wide-Angle "Parabolic" Equation
- Stable Explicit Schemes for Equations of the Schrödinger Type
- Parabolic approximations to the time-independent elastic wave equation
- Reciprocity and energy conservation within the parabolic approximation.