A discrete comparison principle for the time-fractional diffusion equation

DOI10.1016/J.CAMWA.2020.04.018zbMath1447.65018OpenAlexW3033767560MaRDI QIDQ2194811

Martin Stynes, Hu Chen

Publication date: 7 September 2020

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2020.04.018

zbMATH Keywords

convergence analysisweak singularity\(L1\) schemediscrete comparison principle

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) Fractional partial differential equations (35R11)

Related Items (11)

A Survey of the L1 Scheme in the Discretisation of Time-Fractional Problems ⋮ Two-grid finite element methods for nonlinear time-fractional parabolic equations ⋮ Local error estimate of L1 scheme for linearized time fractional KdV equation with weakly singular solutions ⋮ The stability and convergence analysis of finite difference methods for the fractional neutron diffusion equation ⋮ Error analysis of a finite difference method for the distributed order sub-diffusion equation using discrete comparison principle ⋮ Discrete comparison principle of a finite difference method for the multi-term time fractional diffusion equation ⋮ A robust uniformly convergent finite difference scheme for the time-fractional singularly perturbed convection-diffusion problem ⋮ Pointwise error estimate of an alternating direction implicit difference scheme for two-dimensional time-fractional diffusion equation ⋮ An \(\alpha\)-robust error analysis of the \(\overline{\mathrm{L}1}\) scheme for time-fractional integro-differential initial-boundary value problems ⋮ \(\alpha\)-robust \(H^1\)-norm convergence analysis of ADI scheme for two-dimensional time-fractional diffusion equation ⋮ Local \(H^1\)-norm error analysis of a mixed finite element method for a time-fractional biharmonic equation

Cites Work

• A fitted scheme for a Caputo initial-boundary value problem
• On the maximum principle for a time-fractional diffusion equation
• Error analysis of a second-order method on fitted meshes for a time-fractional diffusion problem
• Stability of fully discrete schemes with interpolation-type fractional formulas for distributed-order subdiffusion equations
• An analysis of the Grünwald-Letnikov scheme for initial-value problems with weakly singular solutions
• A Discrete Grönwall Inequality with Applications to Numerical Schemes for Subdiffusion Problems
• 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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