An efficient space-time method for time fractional diffusion equation
From MaRDI portal
Publication:2333736
DOI10.1007/s10915-019-01052-8zbMath1466.65214OpenAlexW2973812666MaRDI QIDQ2333736
Publication date: 13 November 2019
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10915-019-01052-8
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Error bounds for boundary value problems involving PDEs (65N15) Fractional derivatives and integrals (26A33) Fractional partial differential equations (35R11)
Related Items
A space-time spectral method for the inverse source problems of the damped wave equation with memory ⋮ Discretization and analysis of an optimal control of a variable-order time-fractional diffusion equation with pointwise constraints ⋮ The finite volume element method for the two-dimensional space-fractional convection-diffusion equation ⋮ A novel spectral Galerkin/Petrov-Galerkin algorithm for the multi-dimensional space-time fractional advection-diffusion-reaction equations with nonsmooth solutions ⋮ An efficient and accurate numerical method for the fractional optimal control problems with fractional Laplacian and state constraint ⋮ Unconditional convergence of linearized orthogonal spline collocation algorithm for semilinear subdiffusion equation with nonsmooth solution ⋮ A Spectrally Accurate Approximation to Subdiffusion Equations Using the Log Orthogonal Functions ⋮ Accurate numerical simulations for fractional diffusion equations using spectral deferred correction methods ⋮ Spectral Galerkin Approximation of Fractional Optimal Control Problems with Fractional Laplacian ⋮ An efficient spline collocation method for a nonlinear fourth-order reaction subdiffusion equation ⋮ Approximation of an optimal control problem for the time-fractional Fokker-Planck equation ⋮ Optimal error estimates of a time-spectral method for fractional diffusion problems with low regularity data
Cites Work
- Unnamed Item
- Fractional Sturm-Liouville eigen-problems: theory and numerical approximation
- A multi-domain spectral method for time-fractional differential equations
- Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation
- Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
- Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations
- Fourierization of the Legendre-Galerkin method and a new space-time spectral method
- The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
- The accurate solution of Poisson's equation by expansion in Chebyshev polynomials
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- Enriched spectral methods and applications to problems with weakly singular solutions
- A unified Petrov-Galerkin spectral method for fractional PDEs
- A fractional spectral method with applications to some singular problems
- Space-time Petrov-Galerkin FEM for fractional diffusion problems
- Müntz spectral methods for the time-fractional diffusion equation
- Time-fractional diffusion equation in the fractional Sobolev spaces
- Finite difference/spectral approximations for the time-fractional diffusion equation
- Direct solution of partial difference equations by tensor product methods
- A fully discrete difference scheme for a diffusion-wave system
- An analysis of the Grünwald-Letnikov scheme for initial-value problems with weakly singular solutions
- A Petrov--Galerkin Finite Element Method for Fractional Convection-Diffusion Equations
- Generalized Jacobi functions and their applications to fractional differential equations
- Optimal Fractional Integration Preconditioning and Error Analysis of Fractional Collocation Method Using Nodal Generalized Jacobi Functions
- Optimal Error Estimates of Spectral Petrov--Galerkin and Collocation Methods for Initial Value Problems of Fractional Differential Equations
- Generalized Jacobi Spectral-Galerkin Method for Nonlinear Volterra Integral Equations with Weakly Singular Kernels
- Spectral Methods
- A Generalized Spectral Collocation Method with Tunable Accuracy for Variable-Order Fractional Differential Equations
- Two Fully Discrete Schemes for Fractional Diffusion and Diffusion-Wave Equations with Nonsmooth Data
- A Space-Time Spectral Method for the Time Fractional Diffusion Equation
- Spectral Methods and Their Applications
- Time Discretization of a Tempered Fractional Feynman--Kac Equation with Measure Data
- Numerical Analysis of Nonlinear Subdiffusion Equations
- Analysis of a Time-Stepping Scheme for Time Fractional Diffusion Problems with Nonsmooth Data
- Error Analysis of a Finite Element Method for the Space-Fractional Parabolic Equation
- A Space-Time Petrov-Galerkin Spectral Method for Time Fractional Diffusion Equation
- The Use of Finite Difference/Element Approaches for Solving the Time-Fractional Subdiffusion Equation
- Polynomial spectral collocation method for space fractional advection–diffusion equation
- Spectral Methods
- Variational formulation of problems involving fractional order differential operators
