Numerical methods for the two-dimensional multi-term time-fractional diffusion equations

DOI10.1016/j.camwa.2017.07.008zbMath1397.65150OpenAlexW2745111427MaRDI QIDQ1667655

Linlin Zhao, Fawang Liu, V. V. Anh

Publication date: 30 August 2018

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2017.07.008

zbMATH Keywords

fractional Laplace operatormatrix transfer techniquemulti-term time-fractional diffusion 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) Fractional partial differential equations (35R11)

Related Items (12)

Anisotropic $EQ_1^{rot}$ Finite Element Approximation for a Multi-Term Time-Fractional Mixed Sub-Diffusion and Diffusion-Wave Equation ⋮ Reproducing kernel particle method for two-dimensional time-space fractional diffusion equations in irregular domains ⋮ A Legendre spectral method on graded meshes for the two-dimensional multi-term time-fractional diffusion equation with non-smooth solutions ⋮ A robust error analysis of the OSC method for a multi-term fourth-order sub-diffusion equation ⋮ Modified fractional reduced differential transform method for the solution of multiterm time-fractional diffusion equations ⋮ Two-grid fully discrete finite element algorithms on temporal graded meshes for nonlinear multi-term time-fractional diffusion equations with variable coefficient ⋮ Space-time finite element method for the multi-term time-space fractional diffusion equation on a two-dimensional domain ⋮ Coupling of the improved singular boundary method and dual reciprocity method for multi-term time-fractional mixed diffusion-wave equations ⋮ Anisotropic linear triangle finite element approximation for multi-term time-fractional mixed diffusion and diffusion-wave equations with variable coefficient on 2D bounded domain ⋮ Unnamed Item ⋮ On positivity preservation in nonlinear finite volume method for multi-term fractional subdiffusion equation on polygonal meshes ⋮ \(\alpha\)-robust \(H^1\)-norm convergence analysis of ADI scheme for two-dimensional time-fractional diffusion equation

Cites Work

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• Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain
• Two high-order numerical algorithms for solving the multi-term time fractional diffusion-wave equations
• Fractional-in-time and multifractional-in-space stochastic partial differential equations
• A meshless point collocation method for 2-D multi-term time fractional diffusion-wave equation
• Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation
• Convergence and superconvergence of a fully-discrete scheme for multi-term time fractional diffusion equations
• Fractional derivatives for physicists and engineers. Volume I: Background and theory. Volume II: Applications
• The Galerkin finite element method for a multi-term time-fractional diffusion equation
• Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain
• Boundary value problems for multi-term fractional differential equations
• Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Numerical solution of the space fractional Fokker-Planck equation.
• The accuracy and stability of an implicit solution method for the fractional diffusion equation
• A high-order spectral method for the multi-term time-fractional diffusion equations
• Numerical methods for solving the multi-term time-fractional wave-diffusion equation
• Space-time fractional stochastic equations on regular bounded open domains
• Finite difference/spectral approximations for the time-fractional diffusion equation
• Fractional Pearson diffusions
• Time-dependent fractional advection-diffusion equations by an implicit MLS meshless method
• Novel Numerical Methods for Solving the Time-Space Fractional Diffusion Equation in Two Dimensions
• Stochastic models for fractional calculus
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

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