A high-order compact finite difference method on nonuniform time meshes for variable coefficient reaction-subdiffusion problems with a weak initial singularity

DOI10.1007/s10543-020-00841-0zbMath1481.65162OpenAlexW3121588383MaRDI QIDQ2045177

Yanyan Li

Publication date: 12 August 2021

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-020-00841-0

zbMATH Keywords

compact finite difference methodstability and convergencenonuniform time meshweak initial singularityreaction-subdiffusion equations

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) 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) Finite difference methods for boundary value problems involving PDEs (65N06) Fractional partial differential equations (35R11)

Related Items (4)

Global superconvergence analysis of nonconforming finite element method for time fractional reaction-diffusion problem with anisotropic data ⋮ Block-centered finite difference method for a tempered subdiffusion model with time-dependent coefficients ⋮ Regularity theory for fractional reaction–subdiffusion equation and application to inverse problem ⋮ Existence and regularity in inverse source problem for fractional reaction-subdiffusion equation perturbed by locally Lipschitz sources

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• 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
• Compact exponential scheme for the time fractional convection-diffusion reaction equation with variable coefficients
• A new difference scheme for the time fractional diffusion equation
• Summation by parts operators for finite difference approximations of second-derivatives with variable coefficients
• Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
• A finite difference method for an anomalous sub-diffusion equation, theory and applications
• A second-order accurate numerical method for a fractional wave equation
• Numerical simulations of 2D fractional subdiffusion problems
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• 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 compact difference methods for Caputo-type variable coefficient fractional sub-diffusion equations in conservative form
• Convergence in positive time for a finite difference method applied to a fractional convection-diffusion problem
• A fourth order accurate finite difference scheme for the elastic wave equation in second order formulation
• Error analysis of a second-order method on fitted meshes for a time-fractional diffusion problem
• A high-order \(L2\)-compact difference method for Caputo-type time-fractional sub-diffusion equations with variable coefficients
• A fast iterative solver for the variable coefficient diffusion equation on a disk
• An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data
• Error Analysis of a High Order Method for Time-Fractional Diffusion Equations
• Two Fully Discrete Schemes for Fractional Diffusion and Diffusion-Wave Equations with Nonsmooth Data
• An Analysis of the Modified L1 Scheme for Time-Fractional Partial Differential Equations with Nonsmooth Data
• A Discrete Grönwall Inequality with Applications to Numerical Schemes for Subdiffusion Problems
• FEM for time-fractional diffusion equations, novel optimal error analyses
• Sharp Error Estimate of the Nonuniform L1 Formula for Linear Reaction-Subdiffusion Equations
• Efficient compact finite difference methods for a class of time-fractional convection–reaction–diffusion equations with variable coefficients
• Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion
• Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
• Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions

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