Solutions to the discrete Airy equation: application to parabolic equation calculations

DOI10.1016/j.cam.2004.02.011zbMath1060.65092OpenAlexW2104897381MaRDI QIDQ1883481

Ronald E. Mickens, Matthias Ehrhardt

Publication date: 12 October 2004

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2004.02.011

zbMATH Keywords

stabilitynumerical exampleparabolic equationdifference equationunderwater acousticsAiry equationSchrödinger-type equationradar propagationdiscrete transparent boundary condition

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Finite difference methods applied to problems in fluid mechanics (76M20) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Hydro- and aero-acoustics (76Q05)

Related Items (9)

Quantization condition from exact WKB for difference equations ⋮ Discrete non-local boundary conditions for split-step Padé approximations of the one-way Helmholtz equation ⋮ Nonlinear Schrödinger equation and the hyperbolization method ⋮ A Transparent Boundary Condition for an Elastic Bottom in Underwater Acoustics ⋮ Exact transparent boundary conditions for the parabolic wave equations with linear and quadratic potentials ⋮ Analytic discrete transparent boundary conditions for high-order Padé parabolic equations ⋮ Deterministic evolution of an asexual population under the action of beneficial and deleterious mutations on additive fitness landscapes ⋮ Transparent boundary condition for numerical modeling of intense laser-molecule interaction ⋮ Absorbing boundary conditions for the one-dimensional Schrödinger equation with an exterior repulsive potential

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Coulomb and Bessel functions of complex arguments and order
• Ocean acoustic propagation by finite difference methods
• Convolution quadrature and discretized operational calculus. II
• Wave propagation and underwater acoustics
• Discrete transparent boundary conditions for wide angle parabolic equations in underwater acoustics
• Linear algebra, rational approximation and orthogonal polynomials
• Discrete transparent boundary conditions for the Schrödinger equation: fast calculation, approximation, and stability
• Asymptotic solutions to a discrete airy equation
• Asymptotic Expansions for Second-Order Linear Difference Equations, II
• Asymptotic properties of solutions to two discrete airy equations

This page was built for publication: Solutions to the discrete Airy equation: application to parabolic equation calculations