Spectral approximation methods and error estimates for Caputo fractional derivative with applications to initial-value problems
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Publication:726866
DOI10.1016/j.jcp.2016.05.017zbMath1349.65249OpenAlexW2364992128MaRDI QIDQ726866
Wen Cao, Beiping Duan, Zhou-shun Zheng
Publication date: 5 December 2016
Published in: Journal of Computational Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jcp.2016.05.017
Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Fractional ordinary differential equations (34A08)
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Cites Work
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- A meshless method based on point interpolation method (PIM) for the space fractional diffusion equation
- Fractional Sturm-Liouville eigen-problems: theory and numerical approximation
- Crank-Nicolson method for the fractional diffusion equation with the Riesz fractional derivative
- Numerical approaches to fractional calculus and fractional ordinary differential equation
- Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations
- Riesz potential operators and inverses via fractional centred derivatives
- Quadrature rule for Abel's equations: Uniformly approximating fractional derivatives
- Computational algorithms for computing the fractional derivatives of functions
- Matrix approach to discrete fractional calculus. II: Partial fractional differential equations
- On the numerical evaluation of fractional derivatives in multi-degree-of-freedom systems
- An approximate method for numerical solution of fractional differential equations
- The numerical solution of linear multi-term fractional differential equations: Systems of equations
- A high order schema for the numerical solution of the fractional ordinary differential equations
- Algorithms for the fractional calculus: a selection of numerical methods
- Generalized Jacobi functions and their applications to fractional differential equations
- Sharp Error Bounds for Jacobi Expansions and Gegenbauer--Gauss Quadrature of Analytic Functions
- Spectral approximations to the fractional integral and derivative
- Spectral Methods
- Discretized Fractional Calculus
- A Space-Time Spectral Method for the Time Fractional Diffusion Equation
- Convergence analysis of the Jacobi spectral-collocation methods for Volterra integral equations with a weakly singular kernel
- Convergence Analysis of a Block-by-Block Method for Fractional Differential Equations
- A Crank--Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation
- Fractional Spectral Collocation Method
