High-order accurate local schemes for fractional differential equations
type: Item
instance of: scholarly article
title: High-order accurate local schemes for fractional differential equations
zbMATH Open document ID: 1364.65140
author: Daniel Baffet
author: Jan S. Hesthaven
published in: Journal of Scientific Computing
publication date: 2017-03-02T00:00:00Z
full work available at URL: http://infoscience.epfl.ch/record/225936
review text: Various different approaches for the numerical solution of fractional-order differential equations are known today. Most of these methods can be interpreted as generalizations of classical and well-known schemes for first-order differential equations. A particularly frequently occurring example is the classical Adams-Bashforth-Moulton method for which various different ``fractionalizations'' are known. The paper under review adds another completely new algorithm to this collection. The idea is based on a carefully chosen expansion of the unknown solution's fractional derivative. This expansion is constructed in terms of an orthogonal basis of a suitable function space. A convergence analysis is provided, and a Milne-type error indicator is constructed. Based on the latter, the authors then develop and test a stepsize control strategy.
reviewed by: Kai Diethelm
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 65L50
zbMATH DE Number: 6690806
zbMATH Keywords: fractional differential equations
zbMATH Keywords: Volterra equations
zbMATH Keywords: high-order methods
zbMATH Keywords: Adams-Bashforth-Moulton method
zbMATH Keywords: algorithm
zbMATH Keywords: convergence
zbMATH Keywords: Milne-type error indicator
zbMATH Keywords: stepsize control
describes a project that uses: FODE
MaRDI profile type: Publication
OpenAlex ID: W1779031210
cites work: The random walk's guide to anomalous diffusion: A fractional dynamics approach
cites work: The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
cites work: A second-order accurate numerical method for the two-dimensional fractional diffusion equation
cites work: Finite Element Method for the Space and Time Fractional Fokker–Planck Equation
cites work: Variational formulation for the stationary fractional advection dispersion equation
cites work: Stable multi-domain spectral penalty methods for fractional partial differential equations
cites work: Local Discontinuous Galerkin methods for fractional diffusion equations
cites work: Finite difference methods for the time fractional diffusion equation on non-uniform meshes
cites work: Convolution quadrature and discretized operational calculus. I
cites work: Q3750978
cites work: hp-Discontinuous Galerkin Time-Stepping for Volterra Integrodifferential Equations
cites work: An $hp$-Version Discontinuous Galerkin Method for Integro-Differential Equations of Parabolic Type
cites work: A First Course in the Numerical Analysis of Differential Equations
cites work: Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
cites work: An Introduction to Numerical Analysis
cites work: Q3331506
cites work: Polynomial approximation of some singular functions
DOI: 10.1007/S10915-015-0089-1
Recommended article: A High-Order Accuracy Method for Solving the Fractional Diffusion Equations
Recommended article: Fractional high order methods for the nonlinear fractional ordinary differential equation
Recommended article: Numerical Analysis of a High-Order Scheme for Nonlinear Fractional Differential Equations with Uniform Accuracy
Recommended article: High-Order Accurate Runge-Kutta (Local) Discontinuous Galerkin Methods for One- and Two-Dimensional Fractional Diffusion Equations
Recommended article: High-order numerical methods for solving time fractional partial differential equations
Recommended article: High order algorithms for numerical solution of fractional differential equations
Recommended article: High‐order compact schemes for fractional differential equations with mixed derivatives
Recommended article: High-order quasi-compact difference schemes for fractional diffusion equations
Recommended article: A new computational approach for solving nonlinear local fractional PDEs
Recommended article: Local discontinuous Galerkin methods for fractional ordinary differential equations
description: scientific article; zbMATH DE number 6690806