DOAJ Open Access 2022

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 Yulia Belova

Abstrak

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.

Topik & Kata Kunci

Mathematics

Penulis (5)

Alexander Sukhinov

Alexander Chistyakov

Elena Timofeeva

Alla Nikitina

Yulia Belova

Format Sitasi

APA MLA BibTeX

Sukhinov, A., Chistyakov, A., Timofeeva, E., Nikitina, A., Belova, Y. (2022). The Construction and Research of the Modified “Upwind Leapfrog” Difference Scheme with Improved Dispersion Properties for the Korteweg–de Vries Equation. https://doi.org/10.3390/math10162922

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Informasi Jurnal

Tahun Terbit: 2022
Sumber Database: DOAJ
DOI: 10.3390/math10162922
Akses: Open Access ✓