Modified Upwind Leapfrog difference scheme
https://doi.org/10.23947/2587-8999-2020-1-1-56-70
Abstract
The paper considers the application of the scheme based on linear combination of the Upwind and Standard Leapfrog difference schemes with weight coefficients obtained by minimizing the approximation error. According to the resulting error estimation, it is preferable to use the proposed difference scheme with the approximation error О(ch2) for small Courant numbers than the classical Upwind and Standard Leapfrog difference schemes with the approximation errors О(ch2). The paper presents the comparison solution of the transfer problem based on the proposed scheme with the results obtained using the scheme, which is the linear combination of the Upwind Leapfrog and central difference schemes, as well as two-parameter difference scheme with the third order of accuracy.
Keywords
Upwind Leapfrog scheme,
Standard Leapfrog scheme,
central difference scheme,
twoparameter difference scheme,
difference scheme accuracy
Supporting agencies: The reported study was funded by RFBR according to the research project 19-07-00623.
About the Authors
A. I. Sukhinov
Don State Technical University
Russian Federation
Russian Federation
Sukhinov Alexander Ivanovich, Doctor of Science in Physics and Maths, Full professor, Head of a department
Gagarin square, 1, Rostov-on-Don
A. E. Chistyakov
Don State Technical University
Russian Federation
Russian Federation
Chistyakov Alexander Evgenyevich, Doctor of Science in Physics and Maths, Professor
Gagarin square, 1, Rostov-on-Don
I. Y. Kuznetsova
Southern Federal University
Russian Federation
Russian Federation
Kuznetsova Inna Yurevna, Senior lector
Bolshaya Sadovaya Str., 105/42, Rostov-on-Don
E. A. Protsenko
A.P. Chekhov University of Taganrog (branch of Rostov State University of Economics)
Russian Federation
Russian Federation
Protsenko Elena Anatolyevna, Candidate of Science in Physics and Maths, Assistant professor
Initsiativnaya Str. 48, Taganrog
Y. V. Belova
Don State Technical University
Russian Federation
Russian Federation
Belova Yulia Valerievna, Candidate of Science in Physics and Maths
Gagarin square, 1, Rostov-on-Don
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Review
For citations:
Sukhinov A.I., Chistyakov A.E., Kuznetsova I.Y., Protsenko E.A., Belova Y.V. Modified Upwind Leapfrog difference scheme. Computational Mathematics and Information Technologies. 2020;4(1):56-70. https://doi.org/10.23947/2587-8999-2020-1-1-56-70
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