Diffusive Approximation of a Time-Fractional Burger's Equation in Nonlinear Acoustics

DOI10.1137/16M1062491zbMath1443.65275arXiv1602.07205OpenAlexW2962928211MaRDI QIDQ2821707

Bruno Lombard, Denis Matignon

Publication date: 23 September 2016

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1602.07205

zbMATH Keywords

fractional derivativesnonlinear acousticsshock-capturing schemesBurger's equationdiffusive representationStrang splitting

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Nonlinear waves in solid mechanics (74J30) Fractional derivatives and integrals (26A33) First-order nonlinear hyperbolic equations (35L60) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65M99) Fractional partial differential equations (35R11)

Related Items (10)

Energy analysis and discretization of the time-domain equivalent fluid model for wave propagation in rigid porous media ⋮ Asymptotic stability of the multidimensional wave equation coupled with classes of positive-real impedance boundary conditions ⋮ A two-way model for nonlinear acoustic waves in a non-uniform lattice of Helmholtz resonators ⋮ Pointwise error estimates of compact difference scheme for mixed-type time-fractional Burgers' equation ⋮ Analysis and description of the infinite-dimensional nature for nabla discrete fractional order systems ⋮ Analysis of a Sugimoto Model of Nonlinear Acoustics in an Array of Helmholtz Resonators ⋮ Time-local discretization of fractional and related diffusive operators using Gaussian quadrature with applications ⋮ Energy analysis and discretization of nonlinear impedance boundary conditions for the time-domain linearized Euler equations ⋮ Moving least squares particle hydrodynamics method for Burgers' equation ⋮ A new iterative technique for a fractional model of nonlinear Zakharov-Kuznetsov equations via Sumudu transform

Uses Software

• SolvOpt

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