Numerical methods and analysis for a multi-term time-space variable-order fractional advection-diffusion equations and applications

DOI10.1016/J.CAM.2018.12.027zbMath1448.76151OpenAlexW2905890484WikidataQ128714631 ScholiaQ128714631MaRDI QIDQ1736393

Ruige Chen, Fawang Liu, V. V. Anh

Publication date: 26 March 2019

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2018.12.027

zbMATH Keywords

implicit numerical methodsfractional advection-diffusion equationsmodified grid approximation methodmulti-term models

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05) Finite difference methods applied to problems in fluid mechanics (76M20) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Fractional partial differential equations (35R11)

Related Items (16)

Quantifying fate and transport of nitrate in saturated soil systems using fractional derivative model ⋮ An inverse problem to simulate the transport of chloride in concrete by time–space fractional diffusion model ⋮ A hybrid method for solving time fractional advection-diffusion equation on unbounded space domain ⋮ An investigation of space distributed-order models for simulating anomalous transport in a binary medium ⋮ Generalized Bernoulli polynomials: solving nonlinear 2D fractional optimal control problems ⋮ Finite difference/collocation method to solve multi term variable‐order fractional reaction–advection–diffusion equation in heterogeneous medium ⋮ A fully spectral tau method for a class of linear and nonlinear variable-order time-fractional partial differential equations in multi-dimensions ⋮ Efficient numerical methods for the nonlinear two-sided space-fractional diffusion equation with variable coefficients ⋮ Finite difference scheme for a non-linear subdiffusion problem with a fractional derivative along the trajectory of motion ⋮ Generalized shifted Chebyshev polynomials: solving a general class of nonlinear variable order fractional PDE ⋮ Approximation methods for solving fractional equations ⋮ A second-order numerical method for space-time variable-order diffusion equation ⋮ Numerical solution of two-dimensional fractional-order reaction advection sub-diffusion equation with finite-difference Fibonacci collocation method ⋮ An unstructured mesh control volume method for two-dimensional space fractional diffusion equations with variable coefficients on convex domains ⋮ A novel high order compact ADI scheme for two dimensional fractional integro-differential equations ⋮ Multi-term time fractional diffusion equations and novel parameter estimation techniques for chloride ions sub-diffusion in reinforced concrete

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• An implicit numerical method of a new time distributed-order and two-sided space-fractional advection-dispersion equation
• A novel numerical method for the time variable fractional order mobile-immobile advection-dispersion model
• Numerical methods and analysis for a class of fractional advection-dispersion models
• Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain
• Slip effects on MHD flow of a generalized Oldroyd-B fluid with fractional derivative
• Initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation
• Fractional derivatives for physicists and engineers. Volume I: Background and theory. Volume II: Applications
• 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
• Numerical methods for fractional partial differential equations with Riesz space fractional derivatives
• Stability and convergence of the difference methods for the space-time fractional advection-diffusion equation
• Developement of stochastic partial differential equations for subsurface hydrology
• Numerical solution of the space fractional Fokker-Planck equation.
• A time-space spectral tau method for the time fractional cable equation and its inverse problem
• A novel compact numerical method for solving the two-dimensional non-linear fractional reaction-subdiffusion equation
• An historical perspective on fractional calculus in linear viscoelasticity
• Fractional Pearson diffusions
• Finite difference approximations for two-sided space-fractional partial differential equations
• 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
• Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
• Some novel techniques of parameter estimation for dynamical models in biological systems
• Stochastic models for fractional calculus
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

This page was built for publication: Numerical methods and analysis for a multi-term time-space variable-order fractional advection-diffusion equations and applications