Spectral approximation of a variable coefficient fractional diffusion equation in one space dimension
From MaRDI portal
Publication:2279585
DOI10.1016/j.amc.2019.05.017zbMath1429.65289arXiv1810.12420OpenAlexW2899079411MaRDI QIDQ2279585
Xiangcheng Zheng, Vincent J. Ervin, Hong Wang
Publication date: 13 December 2019
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1810.12420
Smoothness and regularity of solutions to PDEs (35B65) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Fractional partial differential equations (35R11)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Efficient and accurate spectral method using generalized Jacobi functions for solving Riesz fractional differential equations
- Accuracy of finite element methods for boundary-value problems of steady-state fractional diffusion equations
- Jacobi approximations in non-uniformly Jacobi-weighted Sobolev spaces
- Finite element approximation for a modified anomalous subdiffusion equation
- A high-accuracy preserving spectral Galerkin method for the Dirichlet boundary-value problem of variable-coefficient conservative fractional diffusion equations
- Efficient spectral-Galerkin methods for fractional partial differential equations with variable coefficients
- Spectral analysis and structure preserving preconditioners for fractional diffusion equations
- Compact finite difference method for the fractional diffusion equation
- A simple finite element method for boundary value problems with a Riemann-Liouville derivative
- A second-order accurate numerical method for the two-dimensional fractional diffusion equation
- Numerical approximation of the fractional Laplacian via \(hp\)-finite elements, with an application to image denoising
- Numerical simulation for conservative fractional diffusion equations by an expanded mixed formulation
- Fractals and fractional calculus in continuum mechanics
- Numerical solution of the space fractional Fokker-Planck equation.
- A unified Petrov-Galerkin spectral method for fractional PDEs
- Spectral analysis and multigrid preconditioners for two-dimensional space-fractional diffusion equations
- A Petrov-Galerkin finite element method for variable-coefficient fractional diffusion equations
- Finite difference approximations for fractional advection-dispersion flow equations
- A superfast-preconditioned iterative method for steady-state space-fractional diffusion equations
- Generalized Jacobi functions and their applications to fractional differential equations
- Wellposedness of Variable-Coefficient Conservative Fractional Elliptic Differential Equations
- Spectral approximations to the fractional integral and derivative
- Spectral Methods for Time-Dependent Problems
- A Spectral Method (of Exponential Convergence) for Singular Solutions of the Diffusion Equation with General Two-Sided Fractional Derivative
- A mixed‐type Galerkin variational formulation and fast algorithms for variable‐coefficient fractional diffusion equations
- Regularity of the solution to 1-D fractional order diffusion equations
- A Fast Finite Difference Method for Two-Dimensional Space-Fractional Diffusion Equations
- Image Denoising Methods. A New Nonlocal Principle
- Inhomogeneous Dirichlet Boundary-Value Problems of Space-Fractional Diffusion Equations and their Finite Element Approximations
- Discontinuous Galerkin Method for Fractional Convection-Diffusion Equations
- Variational formulation for the stationary fractional advection dispersion equation
- Variational formulation of problems involving fractional order differential operators
