@Article{CiCP-29-2,
author = {Kang, Jian and Xinliang, Li},
title = {A Sufficient and Necessary Condition of the Existence of WENO-Like Linear Combination for Finite Difference Schemes},
journal = {Communications in Computational Physics},
year = {2021},
volume = {29},
number = {2},
pages = {534--570},
abstract = {<p style="text-align: justify;">In the finite difference WENO (weighted essentially non-oscillatory) method, the final scheme on the whole stencil was constructed by linear combinations of
highest order accurate schemes on sub-stencils, all of which share the same total count
of grid points. The linear combination method which the original WENO applied was
generalized to arbitrary positive-integer-order derivative on an arbitrary (uniform or
non-uniform) mesh, still applying finite difference method. The possibility of expressing the final scheme on the whole stencil as a linear combination of highest order accurate schemes on WENO-like sub-stencils was investigated. The main results include:
(a) the highest order of accuracy a finite difference scheme can achieve and (b) a sufficient and necessary condition that the linear combination exists. This is a sufficient
and necessary condition for all finite difference schemes in a set (rather than a specific
finite difference scheme) to have WENO-like linear combinations. After the proofs
of the results, some remarks on the WENO schemes and TENO (targeted essentially
non-oscillatory) schemes were given.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2019-0112},
url = {https://global-sci.com/article/79639/a-sufficient-and-necessary-condition-of-the-existence-of-weno-like-linear-combination-for-finite-difference-schemes}
}