Preprocessing schemes for fractional-derivative problems to improve their convergence rates

DOI10.1016/J.AML.2017.05.016zbMath1376.65120OpenAlexW2624862304MaRDI QIDQ2411149

Martin Stynes, José Luis Gracia

Publication date: 20 October 2017

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

Full work available at URL: https://doi.org/10.1016/j.aml.2017.05.016

zbMATH Keywords

convergenceinitial-boundary value problemCaputo derivativeweak singularityL1 schemepreprocessing of solution

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) 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 (7)

A novel discrete fractional Grönwall-type inequality and its application in pointwise-in-time error estimates ⋮ An efficient numerical method for \(q\)-fractional differential equations ⋮ A second-order scheme for a time-fractional diffusion equation ⋮ A graded scheme with bounded grading for a time-fractional Boussinesq type equation ⋮ A Galerkin finite element method for time-fractional stochastic heat equation ⋮ \(\alpha\)-robust \(H^1\)-norm convergence analysis of ADI scheme for two-dimensional time-fractional diffusion equation ⋮ Linearized Galerkin FEMs for nonlinear time fractional parabolic problems with non-smooth solutions in time direction

Cites Work

• Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
• A fitted scheme for a Caputo initial-boundary value problem
• Two Fully Discrete Schemes for Fractional Diffusion and Diffusion-Wave Equations with Nonsmooth Data
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation

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