A Higher Order Resolvent-positive Finite Difference Approximation for Fractional Derivatives

12/15/2021
by   Boris Baeumer, et al.
0

We develop a finite difference approximation of order α for the α-fractional derivative. The weights of the approximation scheme have the same rate-matrix type properties as the popular Grünwald scheme. In particular, approximate solutions to fractional diffusion equations preserve positivity. Furthermore, for the approximation of the solution to the skewed fractional heat equation on a bounded domain the new approximation scheme keeps its order α whereas the order of the Grünwald scheme reduces to order α-1, contradicting the convergence rate results by Meerschaert and Tadjeran.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/07/2022

High Order Numerical Scheme for Generalized Fractional Diffusion Equations

In this paper, a higher order finite difference scheme is proposed for G...
research
06/17/2019

Approximation of Hamilton-Jacobi equations with Caputo time-fractional derivative

In this paper, we investigate the numerical approximation of Hamilton-Ja...
research
01/11/2022

Higher order graded mesh scheme for time fractional differential equations

In this article, we propose a higher order approximation to Caputo fract...
research
09/15/2023

A Finite-Volume Scheme for Fractional Diffusion on Bounded Domains

We propose a new fractional Laplacian for bounded domains, expressed as ...
research
05/27/2021

A unified explicit form for difference formulas for fractional and classical derivatives

A unified explicit form for difference formulas to approximate the fract...
research
02/13/2022

On Generalisation of Isotropic Central Difference for Higher Order Approximation of Fractional Laplacian

The study of generalising the central difference for integer order Lapla...

Please sign up or login with your details

Forgot password? Click here to reset