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https://dspace.ncfu.ru/handle/20.500.12258/21872
Title: | The Construction and Research of the Modified “Upwind Leapfrog” Difference Scheme with Improved Dispersion Properties for the Korteweg–de Vries Equation |
Authors: | Timofeeva, E. F. Тимофеева, Е. Ф. |
Keywords: | Difference “Standard Leapfrog” scheme;Difference “Upwind Leapfrog” scheme;Korteweg–de Vries equation;Mathematical model;Numerical simulation;Parallel computing |
Issue Date: | 2022 |
Publisher: | MDPI |
Citation: | Sukhinov, A., Chistyakov, A., Timofeeva, E., Nikitina, A., Belova, Y. The Construction and Research of the Modified “Upwind Leapfrog” Difference Scheme with Improved Dispersion Properties for the Korteweg–de Vries Equation // Mathematics. - 2022. - Том 10. - Выпуск 16. - Номер статьи 2922. - DOI10.3390/math10162922 |
Series/Report no.: | Mathematics |
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. |
URI: | http://hdl.handle.net/20.500.12258/21872 |
Appears in Collections: | Статьи, проиндексированные в SCOPUS, WOS |
Files in This Item:
File | Description | Size | Format | |
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scopusresults 2336 .pdf Restricted Access | 2.15 MB | Adobe PDF | View/Open | |
WoS 1454 .pdf Restricted Access | 114.87 kB | Adobe PDF | View/Open |
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