A Space-Time Spectral Method for the Time Fractional Diffusion Equation
By Xianjuan Li, Chuanju Xu. SIAM Journal on Numerical Analysis, 2009
724 citations recorded by the source corpus.
Subfields: Modeling and Simulation, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/02bdf52b5b691b45d07cfc89f88a401e5ac83e2b
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Modeling and Simulation
In Numerical Analysis
Citations in the corpus
- Efficient and accurate spectral method using generalized Jacobi functions for solving Riesz fractional differential equations (2016, methodology): “Indeed, spectral methods for some FDEs have been proposed in [11,12] where the well-posedness of some FDEs and their spectral approximations have been established; a Crank–Nicolson ADI Spectral method is presented in [26], a class of efficient spectral methods for solving multi-dimensional FDEs have”
- Spectral Optimization Methods for the Time Fractional Diffusion Inverse Problem (2013, methodology): “Thanks to the weak formulation of TFDE proposed in [8], we are able to derive a space-time spectral method for the considered inverse problem.”
- Existence and Uniqueness of the Weak Solution of the Space-Time Fractional Diffusion Equation and a Spectral Method Approximation (2010, methodology): “6 of [22] under a stronger assumption, i.”
- Error analysis of semidiscrete finite element methods for inhomogeneous time-fractional diffusion (2013, positive): “Li and Xu [13] developed a spectral method in both temporal and spatial variables and established various a priori error estimates.”
- Local discontinuous Galerkin methods for fractional diffusion equations (2013, positive): “While these observations both suggest that it may be worth considering higher order accurate formulation as attractive alternatives, there appears to be very limited work in that direction with a few notable exceptions being [5,16,17] in which spectral methods are used to discretize classical space ”
- A new difference scheme for the time fractional diffusion equation (2014, positive): “Difference schemes of the increased order of approximation such as the compact difference scheme [14, 17, 18, 19] and spectral method [11, 20, 21] were applied to improve the spatial accuracy of fractional diffusion equations.”
- Fourier spectral methods for fractional-in-space reaction-diffusion equations (2014, methodology): “Khader [23] proposes a Chebyshev Galerkin method for the discretisation of the fractional diffusion equation where the spatial derivatives are considered in the Caputo sense, similar to the results of Li and Xu [24] for the time-fractional diffusion equation.”
- A fractional phase-field model for two-phase flows with tunable sharpness: Algorithms and simulations (2016, neutral): “It can be proved [44] lims→1 RLDs x = − lims→1 RL xD = lims→1 Ds x = − lims→1 xD s = ∂ ∂x ,∀x ∈ (a, b).”
- Numerical methods for time-fractional evolution equations with nonsmooth data: A concise overview (2018, background): “In an influential work, Li and Xu [62] proposed a first rigorous space-time formulation for problem (1.”
- A Crank-Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation (2014, methodology): “Up to now, there has been some work on numerical methods for FDEs, such as finite difference methods [12, 20, 26, 47], finite element methods [5, 6, 11, 14, 42], spectral methods [13, 15, 16], and so on [28, 29, 30].”
- A unified Petrov-Galerkin spectral method for fractional PDEs (2015, methodology): “, see [47,29]), one can easily show that it satisfies all the properties of a norm since the Riemann–Liouville fractional derivative of a constant is non-zero.”
- A fractional‐order Jacobi Tau method for a class of time‐fractional PDEs with variable coefficients (2016, positive): “Li and Xu [28, 29] developed a time–space spectral method for time-fractional diffusion.”