Finite difference discretization for one-dimensional higher-order integral fractional Laplacian and its application

A simple and easy-to-implement discrete approximation is proposed for one-dimensional higher-order integral fractional Laplacian (IFL), and our method is applied to discrete the fractional biharmonic equation, multi-term fractional differential model and fractal KdV equation. Based on the generating function, a fractional analogue of the central difference scheme to higher-order IFL is provided, the convergence of the discrete approximation is proved. Extensive numerical experiments are provided to confirm our analytical results. Moreover, some new observations are discovered from our numerical results. (c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

Automated summary

In this study, a simple and easy-to-implement discrete approximation method is proposed for one-dimensional higher-order integral fractional Laplacian (IFL), and it is applied to discretize the fractional biharmonic equation, multi-term fractional differential model, and fractal KdV equation. The convergence of the discrete approximation is proved and extensive numerical experiments are conducted to validate the analytical results. Additionally, new observations are discovered from the numerical results.