Sharp error estimate of a Grünwald-Letnikov scheme for reaction-subdiffusion equations

DOI10.1007/S11075-021-01161-2OpenAlexW3182678341MaRDI QIDQ2118947

Jiwei Zhang, Y. H. Shi, Hu Chen, Yan-Min Zhao

Publication date: 23 March 2022

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-021-01161-2

zbMATH Keywords

Grünwald-Letnikov schemereaction-subdiffusion equationsharp error estimatediscrete fractional Grönwall inequality

Mathematics Subject Classification ID

Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx)

Related Items (4)

Discrete comparison principle of a finite difference method for the multi-term time fractional diffusion equation ⋮ Grünwald-Letnikov scheme for a multi-term time fractional reaction-subdiffusion equation ⋮ A sharp discrete convolution sum estimate ⋮ Sharp error estimate of Grünwald-Letnikov scheme for a multi-term time fractional diffusion equation

Cites Work

• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Numerical analysis of linear and nonlinear time-fractional subdiffusion equations
• Error analysis of a finite element method with GMMP temporal discretisation for a time-fractional diffusion equation
• An analysis of the Grünwald-Letnikov scheme for initial-value problems with weakly singular solutions
• Some Elementary Inequalities Relating to the Gamma and Incomplete Gamma Function
• Numerical Analysis of Nonlinear Subdiffusion Equations
• A Discrete Grönwall Inequality with Applications to Numerical Schemes for Subdiffusion Problems
• Sharp Error Estimate of the Nonuniform L1 Formula for Linear Reaction-Subdiffusion Equations
• Blow-up of error estimates in time-fractional initial-boundary value problems
• Analysis of L1-Galerkin FEMs for Time-Fractional Nonlinear Parabolic Problems
• Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions
• The Use of Finite Difference/Element Approaches for Solving the Time-Fractional Subdiffusion Equation
• Spectral Methods

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