Positivity of Discrete Time-Fractional Operators with Applications to Phase-Field Equations

DOI10.1137/20M1368641OpenAlexW3184132380MaRDI QIDQ5009337

Samir Karaa

Publication date: 20 August 2021

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/20m1368641

zbMATH Keywords

convolutionenergy stable schemepositive quadratic formscompletely monotone sequencediscrete fractional operatorstime-fractional phase-field equation

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integro-partial differential equations (45K05) 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) Positive solutions to PDEs (35B09) Fractional partial differential equations (35R11) Integro-partial differential equations (35R09)

Related Items (6)

Error estimates for approximations of time-fractional biharmonic equation with nonsmooth data ⋮ Unconditional energy dissipation law and optimal error estimate of fast L1 schemes for a time-fractional Cahn-Hilliard problem ⋮ Long time \(H^1\)-stability of fast \(\mathrm{L}2\)-\(1_\sigma\) method on general nonuniform meshes for subdiffusion equations ⋮ Global-in-time \(H^1\)-stability of \(\mathrm{L}2\)-\(1_\sigma\) method on general nonuniform meshes for subdiffusion equation ⋮ A Unified Design of Energy Stable Schemes with Variable Steps for Fractional Gradient Flows and Nonlinear Integro-differential Equations ⋮ Local \(H^1\)-norm error analysis of a mixed finite element method for a time-fractional biharmonic equation

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