Finite Difference Methods for Fractional Differential Equations on Non-Uniform Meshes

DOI10.4208/EAJAM.190520.111020zbMath1476.65186OpenAlexW3130214350WikidataQ115211194 ScholiaQ115211194MaRDI QIDQ5014261

Aijie Cheng, Haili Qiao

Publication date: 1 December 2021

Published in: East Asian Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4208/eajam.190520.111020

zbMATH Keywords

convergence analysisfinite differencenon-uniform meshesfractional differential equationweak singularity

Mathematics Subject Classification ID

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)

Cites Work

• Error estimates of a high order numerical method for solving linear fractional differential equations
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• A fitted scheme for a Caputo initial-boundary value problem
• A second-order scheme for a time-fractional diffusion equation
• A second-order and nonuniform time-stepping maximum-principle preserving scheme for time-fractional Allen-Cahn equations
• A high order schema for the numerical solution of the fractional ordinary differential equations
• The Finite Difference Methods for Fractional Ordinary Differential Equations
• Existence and Uniqueness of the Weak Solution of the Space-time Fractional Diffusion Equation and a Spectral Method Approximation
• Analysis of fractional differential equations

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