A Second-Order Accurate Implicit Difference Scheme for Time Fractional Reaction-Diffusion Equation with Variable Coefficients and Time Drift Term

DOI10.4208/eajam.200618.250319zbMath1462.65120arXiv1707.02679OpenAlexW2980186139MaRDI QIDQ4983623

Xi-Le Zhao, Yong-Liang Zhao, Xian-Ming Gu, Pei-Yong Zhu

Publication date: 26 April 2021

Published in: Unnamed Author (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.02679

zbMATH Keywords

finite difference schemeiterative methodCaputo fractional derivativetime fractional reaction-diffusion equation\(L2-1_\sigma\)-formula

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) 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) Iterative numerical methods for linear systems (65F10) Finite difference methods for boundary value problems involving PDEs (65N06) Preconditioners for iterative methods (65F08) Fractional partial differential equations (35R11)

Related Items (3)

Fast and high-order difference schemes for the fourth-order fractional sub-diffusion equations with spatially variable coefficient under the first Dirichlet boundary conditions ⋮ Galerkin spectral method for a multi-term time-fractional diffusion equation and an application to inverse source problem ⋮ An efficient parallel approximate algorithm for solving time fractional reaction-diffusion equations

Uses Software

• CSparse

Cites Work

• A new difference scheme for the time fractional diffusion equation
• Error estimate for the numerical solution of fractional reaction-subdiffusion process based on a meshless method
• A fractional-order differential equation model of HIV infection of \(CD4^{+}\) T-cells
• Direct Methods for Sparse Linear Systems
• Compact difference method for solving the fractional reaction–subdiffusion equation with Neumann boundary value condition
• Lubich Second-Order Methods for Distributed-Order Time-Fractional Differential Equations with Smooth Solutions

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