A Spectrally Accurate Step-by-Step Method for the Numerical Solution of Fractional Differential Equations
From MaRDI portal
Publication:6493949
DOI10.1007/S10915-024-02517-1MaRDI QIDQ6493949
Luigi Brugnano, Pamela M. Burrage, Felice Iavernaro, Kevin Burrage
Publication date: 29 April 2024
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Fractional derivatives and integrals (26A33) Numerical methods for initial value problems involving ordinary differential equations (65L05) Fractional ordinary differential equations (34A08) Numerical methods for functional-differential equations (65L03)
Cites Work
- Unnamed Item
- A simple framework for the derivation and analysis of effective one-step methods for ODEs
- Fourier spectral methods for fractional-in-space reaction-diffusion equations
- A note on the efficient implementation of Hamiltonian BVMs
- Parallel implementation of block boundary value methods for ODEs
- The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
- Fractional diffusion equations and processes with randomly varying time
- Theory of difference equations: Numerical methods and applications
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- A stable fast time-stepping method for fractional integral and derivative operators
- Numerical solution of fractional differential equations: a survey and a software tutorial
- Detailed error analysis for a fractional Adams method
- Exact solutions to the fractional time-space Bloch-Torrey equation for magnetic resonance imaging
- A general framework for solving differential equations
- A new framework for polynomial approximation to differential equations
- A note on a stable algorithm for computing the fractional integrals of orthogonal polynomials
- Analysis of spectral Hamiltonian boundary value methods (SHBVMs) for the numerical solution of ODE problems
- Trapezoidal methods for fractional differential equations: theoretical and computational aspects
- Line integral solution of differential problems
- Second-order numerical methods for multi-term fractional differential equations: smooth and non-smooth solutions
- Spectrally accurate space-time solution of Hamiltonian PDEs
- Finite difference methods with non-uniform meshes for nonlinear fractional differential equations
- Some error bounds for Gauss-Jacobi quadrature rules
- On the effectiveness of spectral methods for the numerical solution of multi-frequency highly oscillatory Hamiltonian problems
- Line Integral Methods for Conservative Problems
- Discretized Fractional Calculus
- Interpolation Processes
- Error Bounds for Gaussian Quadrature and Weighted-$L^1$ Polynomial Approximation
- Fractional Linear Multistep Methods for Abel-Volterra Integral Equations of the Second Kind
- A New Class of Semi-Implicit Methods with Linear Complexity for Nonlinear Fractional Differential Equations
- Numerical Evaluation of Two and Three Parameter Mittag-Leffler Functions
- Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
- Fast and Oblivious Convolution Quadrature
- (Spectral) Chebyshev collocation methods for solving differential equations
- Iterative Bernstein splines technique applied to fractional order differential equations
This page was built for publication: A Spectrally Accurate Step-by-Step Method for the Numerical Solution of Fractional Differential Equations