Efficient two-dimensional simulations of the fractional Szabo equation with different time-stepping schemes

DOI10.1016/j.camwa.2016.11.018zbMath1412.65091OpenAlexW2559718551MaRDI QIDQ666795

Wen Chen, Wei Cai, Fangying Song, Fanhai Zeng, George Em. Karniadakis

Publication date: 12 March 2019

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2016.11.018

zbMATH Keywords

wave propagationsecond-order convergencefractional diffusion-wave equationdirection splittingviscoelastic media

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) 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) Hydro- and aero-acoustics (76Q05) Fractional partial differential equations (35R11)

Related Items

Fractional Poisson-Nernst-Planck model for ion channels. I: Basic formulations and algorithms ⋮ A Legendre spectral quadrature tau method for the multi-term time-fractional diffusion equations

Cites Work

• Unnamed Item
• A spectral tau algorithm based on Jacobi operational matrix for numerical solution of time fractional diffusion-wave equations
• Second-order approximations for variable order fractional derivatives: algorithms and applications
• High-order algorithms for Riesz derivative and their applications. II
• Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain
• Numerical algorithm with high spatial accuracy for the fractional diffusion-wave equation with von Neumann boundary conditions
• A compact difference scheme for the fractional diffusion-wave equation
• Spectral direction splitting methods for two-dimensional space fractional diffusion equations
• Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients
• Stochastic solutions for fractional wave equations
• Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain
• Fractional relaxation-oscillation and fractional diffusion-wave phenomena.
• Second-order stable finite difference schemes for the time-fractional diffusion-wave equation
• The fundamental solutions for the fractional diffusion-wave equation
• Numerical algorithms for the fractional diffusion-wave equation with reaction term
• The analytical solution and numerical solution of the fractional diffusion-wave equation with damping
• Numerical methods for solving the multi-term time-fractional wave-diffusion equation
• A fully discrete difference scheme for a diffusion-wave system
• Wave simulation in dissipative media described by distributed-order fractional time derivatives
• Fractional diffusion and wave equations
• Fractional differentiation matrices with applications
• A Crank--Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation