High order unconditionally stable difference schemes for the Riesz space-fractional telegraph equation

DOI10.1016/j.cam.2014.09.028zbMath1304.65202OpenAlexW1965128605MaRDI QIDQ475652

Xiao-yun Jiang, Fawang Liu, Ian W. Turner, Shanzhen Chen

Publication date: 27 November 2014

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.2014.09.028

zbMATH Keywords

stabilityPadé approximationdifference schemesemidiscretizationmatrix analysisnumerical resultfractional telegraph equationRiesz fractional operatorspace-fractional hyperbolic equation

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) 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) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Fractional partial differential equations (35R11)

Related Items

Haar wavelets method for time fractional Riesz space telegraph equation with separable solution, Lattice fractional diffusion equation in terms of a Riesz-Caputo difference, Solution of fractional telegraph equation with Riesz space-fractional derivative, Generalized finite difference/spectral Galerkin approximations for the time-fractional telegraph equation, Numerical solution of fractional Riesz space telegraph equation, Finite difference scheme for a fractional telegraph equation with generalized fractional derivative terms, Two efficient spectral methods for the nonlinear fractional wave equation in unbounded domain, Numerical solution of the two-sided space-time fractional telegraph equation via Chebyshev tau approximation, High-order finite difference method based on linear barycentric rational interpolation for Caputo type sub-diffusion equation, Efficient numerical algorithms of time fractional telegraph‐type equations involving Hadamard derivatives, Dissipation-preserving Galerkin-Legendre spectral methods for two-dimensional fractional nonlinear wave equations, A fast and high-order IMEX method for non-linear time-space-fractional reaction-diffusion equations, High-order numerical algorithms for Riesz derivatives via constructing new generating functions, A new fourth-order energy dissipative difference method for high-dimensional nonlinear fractional generalized wave equations, A fourth-order dissipation-preserving algorithm with fast implementation for space fractional nonlinear damped wave equations, A tau method based on Jacobi operational matrix for solving fractional telegraph equation with Riesz-space derivative, An efficient alternating direction implicit finite difference scheme for the three-dimensional time-fractional telegraph equation, A new unconditionally stable method for telegraph equation based on associated Hermite orthogonal functions, An accurate approximate-analytical technique for solving time-fractional partial differential equations, Linearly implicit predictor-corrector methods for space-fractional reaction-diffusion equations with non-smooth initial data, Compact difference scheme for a class of fractional-in-space nonlinear damped wave equations in two space dimensions, An efficient split-step method for distributed-order space-fractional reaction-diffusion equations with time-dependent boundary conditions, A split-step predictor-corrector method for space-fractional reaction-diffusion equations with nonhomogeneous boundary conditions, Shifted fractional-order Jacobi orthogonal functions: application to a system of fractional differential equations, Numerical method to initial-boundary value problems for fractional partial differential equations with time-space variable coefficients, High-order compact difference schemes for the modified anomalous subdiffusion equation, Unconditional energy dissipation and error estimates of the SAV Fourier spectral method for nonlinear fractional generalized wave equation, Construction of new generating function based on linear barycentric rational interpolation for numerical solution of fractional differential equations, Fast structure-preserving difference algorithm for 2D nonlinear space-fractional wave models, A stable explicitly solvable numerical method for the Riesz fractional advection-dispersion equations, Analytical approximation of time-fractional telegraph equation with Riesz space-fractional derivative, Error analysis of fast L1 ADI finite difference/compact difference schemes for the fractional telegraph equation in three dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical methods and analysis for a class of fractional advection-dispersion models
• Theories of thermal stresses based on space-time-fractional telegraph equations
• Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
• An approximate analytical solution of time-fractional telegraph equation
• A fourth-order method of the convection-diffusion equations with Neumann boundary conditions
• A class of fourth-order telegraph-diffusion equations for image restoration
• Compact finite difference method for the fractional diffusion equation
• Unconditionally stable difference schemes for a one-space-dimensional linear hyperbolic equation
• Riesz potential operators and inverses via fractional centred derivatives
• Analytical solution for the time-fractional telegraph equation
• Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
• Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation
• Finite difference approximations for a fractional advection diffusion problem
• The fundamental solutions for the fractional diffusion-wave equation
• Time-fractional telegraph equations and telegraph processes with Brownian time
• Numerical solution of the space fractional Fokker-Planck equation.
• An efficient new perturbative Laplace method for space-time fractional telegraph equations
• The space-fractional telegraph equation and the related fractional telegraph process
• Fractional telegraph equations.
• Finite difference approximations for fractional advection-dispersion flow equations
• Quasi-compact finite difference schemes for space fractional diffusion equations
• Fractional difference/finite element approximations for the time-space fractional telegraph equation
• Stability and convergence of a finite volume method for the space fractional advection-dispersion equation
• Numerical analysis of a two-parameter fractional telegraph equation
• Numerical solution of fractional telegraph equation by using radial basis functions
• An unconditionally stable fourth-order method for telegraph equation based on Hermite interpolation
• Analytical solution for the time-fractional telegraph equation by the method of separating variables
• A fully discrete difference scheme for a diffusion-wave system
• A characteristic difference method for the variable-order fractional advection-diffusion equation
• Analytic and approximate solutions of the space- and time-fractional telegraph equations
• Analytical solution for a generalized space-time fractional telegraph equation
• Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
• A numerical method for the fractional Fitzhugh–Nagumo monodomain model
• On random time and on the relation between wave and telegraph equations