Convergence Outside the Initial Layer for a Numerical Method for the Time-Fractional Heat Equation

DOI10.1007/978-3-319-57099-0_8zbMath1368.65136OpenAlexW2606453112MaRDI QIDQ5274930

Martin Stynes, José Luis Gracia, Eugene O'Riordan

Publication date: 7 July 2017

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-57099-0_8

zbMATH Keywords

finite difference approximationscompatibility conditionsnumerical experimentinitial boundary value problemtime-fractional heat equationCaputo fractional derivative\(L1\) schemelayer regionsmooth and non-smooth data

Mathematics Subject Classification ID

Heat equation (35K05) 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 (4)

Analysis of a finite difference method based on L1 discretization for solving multi‐term fractional differential equation involving weak singularity ⋮ Convergence in positive time for a finite difference method applied to a fractional convection-diffusion problem ⋮ Optimal \(L^\infty (L^2)\) error analysis of a direct discontinuous Galerkin method for a time-fractional reaction-diffusion problem ⋮ Convergence of Finite Difference Method in Positive Time for Multi-Term Time Fractional Differential Equations

Cites Work

• Too much regularity may force too much uniqueness
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data
• Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation

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