Finite volume approximation with ADI scheme and low-rank solver for high dimensional spatial distributed-order fractional diffusion equations

DOI10.1016/j.camwa.2021.02.014OpenAlexW3136826919MaRDI QIDQ2019582

Siu-Long Lei, Lot-Kei Chou

Publication date: 21 April 2021

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

Full work available at URL: https://doi.org/10.1016/j.camwa.2021.02.014

zbMATH Keywords

high dimensionalfinite volume approximationalternating direction implicit schemetensor-train formatdistributed-order

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) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Toeplitz, Cauchy, and related matrices (15B05) Fractional partial differential equations (35R11)

Related Items (3)

Numerical analysis of fractional viscoelastic fluid problem solved by finite difference scheme ⋮ High dimensional Riesz space distributed-order advection-dispersion equations with ADI scheme in compression format ⋮ Divide-and-conquer solver in tensor-train format for \(d\)-dimensional time-space fractional diffusion equations

Uses Software

• Algorithm 862

Cites Work

• Unnamed Item
• Unnamed Item
• Tensor Decompositions and Applications
• Tensor-Train Decomposition
• Novel second-order accurate implicit numerical methods for the Riesz space distributed-order advection-dispersion equations
• Fast preconditioned iterative methods for finite volume discretization of steady-state space-fractional diffusion equations
• Some aspects of fractional diffusion equations of single and distributed order
• On a distributed derivative model of a viscoelastic body
• Fractals and fractional calculus in continuum mechanics
• A numerical method for solving the two-dimensional distributed order space-fractional diffusion equation on an irregular convex domain
• A fast finite difference method for distributed-order space-fractional partial differential equations on convex domains
• A Crank-Nicolson ADI Galerkin-Legendre spectral method for the two-dimensional Riesz space distributed-order advection-diffusion equation
• Two alternating direction implicit spectral methods for two-dimensional distributed-order differential equation
• An efficient finite volume method for nonlinear distributed-order space-fractional diffusion equations in three space dimensions
• Tensor-train format solution with preconditioned iterative method for high dimensional time-dependent space-fractional diffusion equations with error analysis
• Two alternating direction implicit difference schemes for two-dimensional distributed-order fractional diffusion equations
• Distributed-order fractional diffusions on bounded domains
• An efficient algorithm for accelerating the convergence of oscillatory series, useful for computing the polylogarithm and Hurwitz zeta functions
• Finite difference methods for two-dimensional fractional dispersion equation
• Stability and convergence of a Crank-Nicolson finite volume method for space fractional diffusion equations
• Algorithm 862
• A Multilinear Singular Value Decomposition
• Spectral Analysis and Multigrid Methods for Finite Volume Approximations of Space-Fractional Diffusion Equations
• A numerical investigation of the time distributed-order diffusion model
• Boundary Problems for the Fractional and Tempered Fractional Operators
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

This page was built for publication: Finite volume approximation with ADI scheme and low-rank solver for high dimensional spatial distributed-order fractional diffusion equations