A class of efficient time-stepping methods for multi-term time-fractional reaction-diffusion-wave equations

DOI10.1016/j.apnum.2021.02.007zbMath1475.65136OpenAlexW3131102658MaRDI QIDQ2029109

Baoli Yin, Yang Liu, Hong Li, Fanhai Zeng

Publication date: 3 June 2021

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2021.02.007

zbMATH Keywords

fast algorithmcorrection termstime-stepping methodsshifted convolution quadraturefractional reaction-diffusion-wave equation

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) 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) 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) Numerical integration (65D30) Fractional partial differential equations (35R11)

Related Items (12)

Efficient time second-order SCQ formula combined with a mixed element method for a nonlinear time fractional wave model ⋮ Local discontinuous Galerkin method based on a family of second-order time approximation schemes for fractional mobile/immobile convection-diffusion equations ⋮ Mixed finite element algorithm for a nonlinear time fractional wave model ⋮ A novel spectral Galerkin/Petrov-Galerkin algorithm for the multi-dimensional space-time fractional advection-diffusion-reaction equations with nonsmooth solutions ⋮ An alternating direction implicit compact finite difference scheme for the multi-term time-fractional mixed diffusion and diffusion-wave equation ⋮ A fast time stepping Legendre spectral method for solving fractional cable equation with smooth and non-smooth solutions ⋮ Finite element algorithm with a second‐order shifted composite numerical integral formula for a nonlinear time fractional wave equation ⋮ Two high-order compact difference schemes with temporal graded meshes for time-fractional Black-Scholes equation ⋮ Fourth-order compact difference schemes for the two-dimensional nonlinear fractional mobile/immobile transport models ⋮ Fast high-order compact difference scheme for the nonlinear distributed-order fractional Sobolev model appearing in porous media ⋮ A local meshless method for solving multi-dimensional Galilei invariant fractional advection-diffusion equation ⋮ The efficient alternating direction implicit Galerkin method for the nonlocal diffusion-wave equation in three dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation
• Stability and convergence of finite difference schemes for a class of time-fractional sub-diffusion equations based on certain superconvergence
• Too much regularity may force too much uniqueness
• Finite element methods based on two families of second-order numerical formulas for the fractional cable model with smooth solutions
• Galerkin finite element methods for parabolic problems
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Time-fractional telegraph equations and telegraph processes with Brownian time
• A stable fast time-stepping method for fractional integral and derivative operators
• Some second-order \(\theta\) schemes combined with finite element method for nonlinear fractional cable equation
• Finite difference approximations for fractional advection-dispersion flow equations
• An unstructured mesh finite element method for solving the multi-term time fractional and Riesz space distributed-order wave equation on an irregular convex domain
• Necessity of introducing non-integer shifted parameters by constructing high accuracy finite difference algorithms for a two-sided space-fractional advection-diffusion model
• A structure preserving difference scheme with fast algorithms for high dimensional nonlinear space-fractional Schrödinger equations
• Finite difference/finite element method for a novel 2D multi-term time-fractional mixed sub-diffusion and diffusion-wave equation on convex domains
• A class of shifted high-order numerical methods for the fractional mobile/immobile transport equations
• Second-order numerical methods for multi-term fractional differential equations: smooth and non-smooth solutions
• An explicit form for higher order approximations of fractional derivatives
• Novel numerical analysis of multi-term time fractional viscoelastic non-Newtonian fluid models for simulating unsteady MHD Couette flow of a generalized Oldroyd-B fluid
• Stability of a numerical method for a space-time-fractional telegraph equation
• An accurate and efficient algorithm for the time-fractional molecular beam epitaxy model with slope selection
• Discretized Fractional Calculus
• An alternating direction implicit fractional trapezoidal rule type difference scheme for the two-dimensional fractional evolution equation
• Two Fully Discrete Schemes for Fractional Diffusion and Diffusion-Wave Equations with Nonsmooth Data
• Correction of High-Order BDF Convolution Quadrature for Fractional Evolution Equations
• A New Class of Semi-Implicit Methods with Linear Complexity for Nonlinear Fractional Differential Equations
• A new second-order midpoint approximation formula for Riemann–Liouville derivative: algorithm and its application
• Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations
• Efficient Multistep Methods for Tempered Fractional Calculus: Algorithms and Simulations
• A class of second order difference approximations for solving space fractional diffusion equations
• High-Order Approximation to Caputo Derivatives and Caputo-type Advection–Diffusion Equations: Revisited
• The Use of Finite Difference/Element Approaches for Solving the Time-Fractional Subdiffusion Equation
• Optimizing Talbot’s Contours for the Inversion of the Laplace Transform
• Fast and Oblivious Convolution Quadrature

This page was built for publication: A class of efficient time-stepping methods for multi-term time-fractional reaction-diffusion-wave equations