A preconditioned fast finite element approximation to variable-order time-fractional diffusion equations in multiple space dimensions
From MaRDI portal
Publication:1995955
DOI10.1016/j.apnum.2021.01.001zbMath1471.65144OpenAlexW3118925173MaRDI QIDQ1995955
Xiangcheng Zheng, Jinhong Jia, Hong Wang
Publication date: 2 March 2021
Published in: Applied Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.apnum.2021.01.001
finite element methodToeplitz matrixdivided-and-conquer algorithmvariable-order time-fractional diffusion equation
Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Iterative numerical methods for linear systems (65F10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multilinear algebra, tensor calculus (15A69) Toeplitz, Cauchy, and related matrices (15B05) Preconditioners for iterative methods (65F08) Fractional partial differential equations (35R11)
Related Items
Numerical discretization and fast approximation of a variably distributed-order fractional wave equation, All-at-once method for variable-order time fractional diffusion equations, Numerical analysis of a fast finite element method for a hidden-memory variable-order time-fractional diffusion equation, Numerical calculation and fast method for the magnetohydrodynamic flow and heat transfer of fractional Jeffrey fluid on a two-dimensional irregular convex domain, Efficient finite difference scheme for a hidden-memory variable-order time-fractional diffusion equation, Controllability of nonlinear fractional evolution systems in Banach spaces: a survey, A fast numerical scheme for a variably distributed-order time-fractional diffusion equation and its analysis, An L1 type difference/Galerkin spectral scheme for variable-order time-fractional nonlinear diffusion-reaction equations with fixed delay
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Solving the time-fractional Schrödinger equation by Krylov projection methods
- Second-order approximations for variable order fractional derivatives: algorithms and applications
- Numerical techniques for the variable-order time fractional diffusion equation
- A preconditioned fast finite difference method for space-time fractional partial differential equations
- Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
- A divide-and-conquer fast finite difference method for space-time fractional partial differential equation
- Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients
- Galerkin finite element methods for parabolic problems
- A fast method for variable-order space-fractional diffusion equations
- Numerical simulation for conservative fractional diffusion equations by an expanded mixed formulation
- A note on the well-posedness of terminal value problems for fractional differential equations
- Reprint of: boundary conditions for fractional diffusion
- Variable order and distributed order fractional operators
- A direct \(O(N \log ^{2} N)\) finite difference method for fractional diffusion equations
- A fast finite volume method for conservative space-time fractional diffusion equations discretized on space-time locally refined meshes
- Block structured preconditioners in tensor form for the all-at-once solution of a finite volume fractional diffusion equation
- A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications
- High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations. II
- A fast direct method for block triangular Toeplitz-like with tri-diagonal block systems from time-fractional partial differential equations
- Finite element simulation and efficient algorithm for fractional Cahn-Hilliard equation
- The finite difference approximation for a class of fractional sub-diffusion equations on a space unbounded domain
- Wellposedness and regularity of the variable-order time-fractional diffusion equations
- A Generalized Spectral Collocation Method with Tunable Accuracy for Variable-Order Fractional Differential Equations
- Numerical Methods for the Variable-Order Fractional Advection-Diffusion Equation with a Nonlinear Source Term
- Regularity of the solution to 1-D fractional order diffusion equations
- Limit theorem for continuous-time random walks with two time scales
- FINITE DIFFERENCE SCHEMES FOR VARIABLE-ORDER TIME FRACTIONAL DIFFUSION EQUATION
- A Fast Finite Volume Method on Locally Refined Meshes for Fractional Diffusion Equations
- Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations
- Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations: A Second-Order Scheme
- Finite Element Method for the Space and Time Fractional Fokker–Planck Equation
- Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
- Preconditioned Iterative Methods for Two-Dimensional Space-Fractional Diffusion Equations
- Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions
- Fractional Spectral Collocation Method
- Stochastic models for fractional calculus
- The random walk's guide to anomalous diffusion: A fractional dynamics approach
