High-order accurate local schemes for fractional differential equations

DOI10.1007/s10915-015-0089-1zbMath1364.65140OpenAlexW1779031210MaRDI QIDQ514460

Daniel Baffet, Jan S. Hesthaven

Publication date: 2 March 2017

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: http://infoscience.epfl.ch/record/225936

zbMATH Keywords

algorithmconvergencehigh-order methodsfractional differential equationsstepsize controlVolterra equationsAdams-Bashforth-Moulton methodMilne-type error indicator

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50) Fractional ordinary differential equations (34A08)

Related Items (7)

Convergence and stability in maximum norms of linearized fourth-order conservative compact scheme for Benjamin-Bona-Mahony-Burgers' equation ⋮ Efficient high-order exponential time differencing methods for nonlinear fractional differential models ⋮ Unnamed Item ⋮ The unified theory of shifted convolution quadrature for fractional calculus ⋮ The finite difference/finite volume method for solving the fractional diffusion equation ⋮ A posteriori error analysis for a fractional differential equation ⋮ Anomalous diffusion, dilation, and erosion in image processing

Uses Software

• FODE

Cites Work

• Stable multi-domain spectral penalty methods for fractional partial differential equations
• Finite difference methods for the time fractional diffusion equation on non-uniform meshes
• A second-order accurate numerical method for the two-dimensional fractional diffusion equation
• Convolution quadrature and discretized operational calculus. I
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• An $hp$-Version Discontinuous Galerkin Method for Integro-Differential Equations of Parabolic Type
• Polynomial approximation of some singular functions
• A First Course in the Numerical Analysis of Differential Equations
• The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
• An Introduction to Numerical Analysis
• Finite Element Method for the Space and Time Fractional Fokker–Planck Equation
• Local Discontinuous Galerkin methods for fractional diffusion equations
• hp-Discontinuous Galerkin Time-Stepping for Volterra Integrodifferential Equations
• Variational formulation for the stationary fractional advection dispersion equation
• The random walk's guide to anomalous diffusion: A fractional dynamics approach
• Unnamed Item
• Unnamed Item

This page was built for publication: High-order accurate local schemes for fractional differential equations