Using complete monotonicity to deduce local error estimates for discretisations of a multi-term time-fractional diffusion equation

DOI10.1515/CMAM-2021-0053zbMath1484.65175OpenAlexW3191040730MaRDI QIDQ2113842

Hu Chen, Martin Stynes

Publication date: 14 March 2022

Published in: Computational Methods in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/cmam-2021-0053

zbMATH Keywords

local error estimatescomplete monotonicityGrünwald-Letnikov schemeL1 schememulti-term time-fractional

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) Fractional partial differential equations (35R11)

Related Items (6)

A Survey of the L1 Scheme in the Discretisation of Time-Fractional Problems ⋮ A posteriori error analysis for variable-coefficient multiterm time-fractional subdiffusion equations ⋮ Error analysis of a finite difference method for the distributed order sub-diffusion equation using discrete comparison principle ⋮ Local analysis of L1-finite difference method on graded meshes for multi-term two-dimensional time-fractional initial-boundary value problem with Neumann boundary conditions ⋮ Pointwise-in-time error estimate of an ADI scheme for two-dimensional multi-term subdiffusion equation ⋮ Sharp error estimate of Grünwald-Letnikov scheme for a multi-term time fractional diffusion equation

Cites Work

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• An analysis of galerkin proper orthogonal decomposition for subdiffusion
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• A note on deconvolution with completely monotone sequences and discrete fractional calculus
• A Discrete Grönwall Inequality with Applications to Numerical Schemes for Subdiffusion Problems
• Sharp Error Estimate of the Nonuniform L1 Formula for Linear Reaction-Subdiffusion Equations
• Blow-up of error estimates in time-fractional initial-boundary value problems
• Error Analysis for a Fractional-Derivative Parabolic Problem on Quasi-Graded Meshes using Barrier Functions
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
• Spectral Methods

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