The Construction and Research of the Modified “Upwind Leapfrog” Difference Scheme with Improved Dispersion Properties for the Korteweg–de Vries Equation

Alexander Sukhinov, Alexander Chistyakov, Elena Timofeeva, Alla Nikitina and Yulia Belova ()
Additional contact information
Alexander Sukhinov: Department of Mathematics and Informatics, Don State Technical University, 344000 Rostov-on-Don, Russia
Alexander Chistyakov: Department of Mathematics and Informatics, Don State Technical University, 344000 Rostov-on-Don, Russia
Elena Timofeeva: Department of Computational Mathematics and Cybernetics, North Caucasus Federal University, 355017 Stavropol, Russia
Alla Nikitina: Department of Mathematics and Informatics, Don State Technical University, 344000 Rostov-on-Don, Russia
Yulia Belova: Department of Mathematics and Informatics, Don State Technical University, 344000 Rostov-on-Don, Russia

Mathematics, 2022, vol. 10, issue 16, 1-15

Abstract: This paper covers the construction and research of a scheme to solve the problem with nonlinear dispersion wave equations, described by the model Korteweg–de Vries equation. The article proposes approximating the equation based on improved “Upwind Leapfrog” schemes. Its difference operator is a linear combination of operators of the “Standard Leapfrog” and “Upwind Leapfrog” difference schemes, while the modified scheme is obtained from schemes with optimal weight coefficients. Combining certain values of the weight coefficients mutually compensates for approximation errors. In addition, the modified scheme acquires better properties compared with the original schemes. The results of test calculations of solutions of the nonlinear Korteweg–de Vries equation are presented, illustrating the advantages of the modified scheme.

Keywords: mathematical model; Korteweg–de Vries equation; numerical simulation; difference “Upwind Leapfrog” scheme; difference “Standard Leapfrog” scheme; parallel computing (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/16/2922/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/16/2922/ (text/html)

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:gam:jmathe:v:10:y:2022:i:16:p:2922-:d:887568

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().