Structural schemes for one dimension stationary equations
Stéphane Clain,
Rui M.S. Pereira,
Paulo A. Pereira and
Diogo Lopes
Applied Mathematics and Computation, 2023, vol. 457, issue C
Abstract:
In this paper, we propose a new paradigm for finite differences numerical methods, based on compact schemes to provide high order accurate approximations of a smooth solution. The method involves its derivatives approximations at the grid points and the construction of structural equations deriving from the kernels of a matrix that gathers the variables belonging to a small stencil. Numerical schemes involve combinations of physical equations and the structural relations. We have analysed the spectral resolution of the most common structural equations and performed numerical tests to address both the stability and accuracy issues for popular linear and non-linear problems. Several benchmarks are presented that ensure that the developed technology can cope with several problems that may involve non-linearity.
Keywords: Structural equation; Compact scheme; Very high-order; Finite difference (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations:
Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300323003764
Full text for ScienceDirect subscribers only
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:457:y:2023:i:c:s0096300323003764
DOI: 10.1016/j.amc.2023.128207
Access Statistics for this article
Applied Mathematics and Computation is currently edited by Theodore Simos
More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().