A compact finite difference scheme for variable order subdiffusion equation

DOI10.1016/j.cnsns.2016.12.022OpenAlexW2563888514MaRDI QIDQ2005434

Yanan Qiu, Guojie Song, Jian-Xiong Cao

Publication date: 7 October 2020

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2016.12.022

zbMATH Keywords

compact finite difference schemestability and convergencevariable orderfractional subdiffusion equation

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)

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Cites Work

• Unnamed Item
• A high order numerical scheme for variable order fractional ordinary differential equation
• A new fractional numerical differentiation formula to approximate the Caputo fractional derivative and its applications
• Compact difference schemes for the modified anomalous fractional sub-diffusion equation and the fractional diffusion-wave equation
• A new difference scheme for the time fractional diffusion equation
• Fractional spectral collocation methods for linear and nonlinear variable order FPDEs
• Numerical techniques for the variable-order time fractional diffusion equation
• A compact finite difference scheme for the fractional sub-diffusion equations
• Compact finite difference method for the fractional diffusion equation
• A high-order compact finite difference scheme for the fractional sub-diffusion equation
• Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• The accuracy and stability of an implicit solution method for the fractional diffusion equation
• Variable order and distributed order fractional operators
• Statistical physics of dynamical systems with variable memory
• A fractional diffusion equation to describe Lévy flights
• High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations. II
• Finite difference/spectral approximations for the time-fractional diffusion equation
• A Fourier method for the fractional diffusion equation describing sub-diffusion
• Weighted average finite difference methods for fractional diffusion equations
• Numerical Schemes with High Spatial Accuracy for a Variable-Order Anomalous Subdiffusion Equation
• A Generalized Spectral Collocation Method with Tunable Accuracy for Variable-Order Fractional Differential Equations
• Numerical Algorithms for Time-Fractional Subdiffusion Equation with Second-Order Accuracy
• Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
• Integration and differentiation to a variable fractional order
• FINITE DIFFERENCE SCHEMES FOR VARIABLE-ORDER TIME FRACTIONAL DIFFUSION EQUATION
• Fractional diffusion in inhomogeneous media
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

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