Finite difference scheme for multi-term variable-order fractional diffusion equation

DOI10.1186/s13662-018-1544-8zbMath1445.65041OpenAlexW2794714757MaRDI QIDQ1711748

Shujuan Lü, Wenping Chen, Hu Chen, Tao Xu

Publication date: 18 January 2019

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-018-1544-8

zbMATH Keywords

stabilityconvergencedifference schemevariable-order fractional derivativesmulti-term fractional diffusion equation

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) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractional partial differential equations (35R11)

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Cites Work

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• Maximum principles for multi-term space-time variable-order fractional diffusion equations and their applications
• Numerical solution for the variable order linear cable equation with Bernstein polynomials
• Numerical analysis of a new space-time variable fractional order advection-dispersion equation
• A novel numerical method for the time variable fractional order mobile-immobile advection-dispersion model
• Numerical algorithm for the variable-order Caputo fractional functional differential equation
• Second-order approximations for variable order fractional derivatives: algorithms and applications
• Fractional spectral collocation methods for linear and nonlinear variable order FPDEs
• Numerical techniques for the variable-order time fractional diffusion equation
• Numerical solution for a class of nonlinear variable order fractional differential equations with Legendre wavelets
• Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation
• Highly accurate numerical schemes for multi-dimensional space variable-order fractional Schrödinger equations
• The Galerkin finite element method for a multi-term time-fractional diffusion equation
• A new reproducing kernel method for variable order fractional boundary value problems for functional differential equations
• A multi-term fractional diffusion equation for oxygen delivery through a capillary to tissues
• Stability and convergence of a new explicit finite-difference approximation for the variable-order nonlinear fractional diffusion equation
• Design of variable and adaptive fractional order FIR differentiators
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• The temporal second order difference schemes based on the interpolation approximation for solving the time multi-term and distributed-order fractional sub-diffusion equations
• Finite difference approximations for fractional advection-dispersion flow equations
• A compact finite difference scheme for variable order subdiffusion equation
• A numerical technique for variable fractional functional boundary value problems
• Numerical studies for the variable-order nonlinear fractional wave equation
• Numerical methods for solving the multi-term time-fractional wave-diffusion equation
• Maximum principle and numerical method for the multi-term time-space Riesz-Caputo fractional differential equations
• Numerical Schemes with High Spatial Accuracy for a Variable-Order Anomalous Subdiffusion Equation
• Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
• Mechanics with variable-order differential operators
• Numerical Solution to the Multi-Term Time Fractional Diffusion Equation in a Finite Domain