Numerical algorithm based on an implicit fully discrete local discontinuous Galerkin method for the fractional diffusion-wave equation

DOI10.1007/S11075-014-9827-YzbMath1307.65130OpenAlexW2018183327MaRDI QIDQ478200

Huiya Dai, Xindong Zhang, Leilei Wei

Publication date: 3 December 2014

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-014-9827-y

zbMATH Keywords

stabilityconvergencenumerical exampleerror estimatefractional diffusion-wave equationlocal discontinuous Galerkin method

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11) Initial-boundary value problems for PDEs of mixed type (35M13)

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Uses Software

• FODE

Cites Work

• Unnamed Item
• High-order finite element methods for time-fractional partial differential equations
• A compact difference scheme for the fractional diffusion-wave equation
• Numerical approximation of nonlinear fractional differential equations with subdiffusion and superdiffusion
• Generalized differential transform method for solving a space- and time-fractional diffusion-wave equation
• The variational iteration method: an efficient scheme for handling fractional partial differential equations in fluid mechanics
• Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation
• Implicit finite difference approximation for time fractional diffusion equations
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• Time fractional advection-dispersion equation
• Least squares finite-element solution of a fractional order two-point boundary value problem
• Analysis for one-dimensional time-fractional Tricomi-type equations by LDG methods
• Finite difference/spectral approximations for the time-fractional diffusion equation
• Finite difference methods and a Fourier analysis for the fractional reaction-subdiffusion equation
• A fully discrete difference scheme for a diffusion-wave system
• An explicit and numerical solutions of the fractional KdV equation
• Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids
• A Central Difference Numerical Scheme for Fractional Optimal Control Problems
• Fractional diffusion and wave equations
• Applications of variational iteration and homotopy perturbation methods to obtain exact solutions for time‐fractional diffusion‐wave equations
• A Local Discontinuous Galerkin Method for the Camassa–Holm Equation
• The fractional diffusion equation
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Response of a diffusion‐wave system subjected to deterministic and stochastic fields
• Finite Element Method for the Space and Time Fractional Fokker–Planck Equation

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