@Article{EAJAM-13-2,
author = {Zhang, Yan and Liang, Li and Zhu, Jun},
title = {High-Order Multi-Resolution WENO Schemes with Lax-Wendroff Method for Fractional Differential Equations},
journal = {East Asian Journal on Applied Mathematics},
year = {2023},
volume = {13},
number = {2},
pages = {320--339},
abstract = {<p style="text-align: justify;">New high-order finite difference multi-resolution weighted essentially non-oscillatory (WENO) schemes with the Lax-Wendroff (LW) time discretization method
for solving fractional differential equations with the Caputo fractional derivative are
considered. The fractional derivative of order $α ∈ (1, 2)$ is split into an integral part and
a second derivative term. The Gauss-Jacobi quadrature method is employed to solve
the integral part, and a new multi-resolution WENO method for discretizing the second
derivative term is developed. High-order spatial reconstruction procedures use any positive numbers (with a minor restriction) as linear weights. The new multi-resolution
WENO-LW methods are one-step explicit high-order finite difference schemes. They are
more compact than multi-resolution WENO-RK schemes of the same order. The LW time
discretization is more cost efficient than the Runge-Kutta time discretization method.
The construction of new multi-resolution WENO-LW schemes is simple and easy to generalize to arbitrary high-order accuracy in multi-dimensions. One- and two-dimensional
examples with strong discontinuities verify the good performance of new fourth-, sixth-,
and eighth-order multi-resolution WENO-LW schemes.</p>},
issn = {2079-7370},
doi = {https://doi.org/10.4208/eajam.2022-202.260922},
url = {https://global-sci.com/article/82421/high-order-multi-resolution-weno-schemes-with-lax-wendroff-method-for-fractional-differential-equations}
}