A high-order \(L2\)-compact difference method for Caputo-type time-fractional sub-diffusion equations with variable coefficients

DOI10.1016/j.amc.2018.09.007zbMath1429.65201OpenAlexW2893426469MaRDI QIDQ2008016

Lei Ren, Yuan-Ming Wang

Publication date: 22 November 2019

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2018.09.007

zbMATH Keywords

energy methodfractional sub-diffusion equationvariable coefficienthigh-order convergencecompact difference method

Mathematics Subject Classification ID

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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11)

Related Items (15)

Analysis of stability and convergence for L-type formulas combined with a spatial finite element method for solving subdiffusion problems ⋮ Compact scheme for fractional diffusion-wave equation with spatial variable coefficient and delays ⋮ A fast temporal second‐order difference scheme for the time‐fractional subdiffusion equation ⋮ Analysis of a high-order compact finite difference method for Robin problems of time-fractional sub-diffusion equations with variable coefficients ⋮ A local discontinuous Galerkin method for time-fractional diffusion equations ⋮ A novel high-order finite-difference method for the time-fractional diffusion equation with smooth/nonsmooth solutions ⋮ Parameter estimation for time-fractional Black-Scholes equation with S\&P 500 index option ⋮ An operator splitting method for multi-asset options with the Feynman-Kac formula ⋮ Some high order formulae for approximating Caputo fractional derivatives ⋮ A high-order L2 type difference scheme for the time-fractional diffusion equation ⋮ A high-order compact finite difference method on nonuniform time meshes for variable coefficient reaction-subdiffusion problems with a weak initial singularity ⋮ An implicit semi-linear discretization of a bi-fractional Klein-Gordon-Zakharov system which conserves the total energy ⋮ Two energy-preserving numerical models for a multi-fractional extension of the Klein-Gordon-Zakharov system ⋮ Some numerical extrapolation methods for the fractional sub-diffusion equation and fractional wave equation based on the \(L1\) Formula ⋮ Stability and Convergence Analyses of the FDM Based on Some L-Type Formulae for Solving the Subdiffusion Equation

Cites Work

• Unnamed Item
• Unnamed Item
• A compact difference scheme for fractional sub-diffusion equations with the spatially variable coefficient under Neumann boundary conditions
• Combined compact difference scheme for the time fractional convection-diffusion equation with variable coefficients
• A discontinuous Galerkin method for time fractional diffusion equations with variable coefficients
• Error analysis of a high-order compact ADI method for two-dimensional fractional convection-subdiffusion equations
• A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications
• Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation
• Compact exponential scheme for the time fractional convection-diffusion reaction equation with variable coefficients
• A new difference scheme for the time fractional diffusion equation
• An implicit RBF meshless approach for time fractional diffusion equations
• Finite element approximation for a modified anomalous subdiffusion equation
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• An almost monotone approximation for a nonlinear two-point boundary value problem
• Efficient numerical schemes for fractional sub-diffusion equation with the spatially variable coefficient
• High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations. II
• Compact Crank-Nicolson schemes for a class of fractional Cattaneo equation in inhomogeneous medium
• Finite difference/spectral approximations for the time-fractional diffusion equation
• A fast iterative solver for the variable coefficient diffusion equation on a disk
• A fully discrete difference scheme for a diffusion-wave system
• Error Analysis of a High Order Method for Time-Fractional Diffusion Equations
• A finite element method for time fractional partial differential equations
• FEM for time-fractional diffusion equations, novel optimal error analyses
• An Explicit Finite Difference Method and a New von Neumann-Type Stability Analysis for Fractional Diffusion Equations
• High Order Difference Methods for Time Dependent PDE
• The random walk's guide to anomalous diffusion: A fractional dynamics approach
• High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations. III.

This page was built for publication: A high-order \(L2\)-compact difference method for Caputo-type time-fractional sub-diffusion equations with variable coefficients