On decomposition of the fundamental solution of the Helmholtz equation over solutions of iterative parabolic equations

DOI10.3233/ASY-211679MaRDI QIDQ5029356

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Publication date: 14 February 2022

Published in: Asymptotic Analysis (Search for Journal in Brave)

zbMATH Keywords

Helmholtz equationmultiple scalesparaxial approximationiterative parabolic equationspattern solver toolself-starterwide-angle parabolic equations

Mathematics Subject Classification ID

PDEs in connection with optics and electromagnetic theory (35Q60) PDEs in connection with fluid mechanics (35Q35) Padé approximation (41A21) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Series expansions (e.g., Taylor, Lidstone series, but not Fourier series) (41A58) Parabolic equations and parabolic systems (35K99) Axially symmetric solutions to PDEs (35B07)

Uses Software

• WolframAlpha
• OASES

Cites Work

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• A direct multiple-scale approach to the parabolic equation method
• Transparent boundary conditions for iterative high-order parabolic equations
• Computational Ocean Acoustics
• A generalization of the parabolic equation of diffraction theory

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