Unconditional convergence of a fast two-level linearized algorithm for semilinear subdiffusion equations

DOI10.1007/s10915-019-00927-0zbMath1450.65078arXiv1803.09858OpenAlexW3099925677WikidataQ128349127 ScholiaQ128349127MaRDI QIDQ2316208

Jiwei Zhang, Hong-lin Liao, Yonggui Yan

Publication date: 26 July 2019

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.09858

zbMATH Keywords

unconditional convergence semilinear subdiffusion equation discrete fractional Grönwall inequality discrete $H^2$ energy method two-level $L_1$ formula

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) Finite difference methods for boundary value problems involving PDEs (65N06) Fractional partial differential equations (35R11)

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Cites Work