Geodesic
Upwind and Standard Leapfrog Difference Schemes
Numerical methods and programming, Tome 20 (2019) no. 2, pp. 170-181.

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In order to solve the transfer problem, it is proposed to use the scheme based on a linear combination of the Upwind and Standard Leapfrog difference schemes with weighting coefficients obtained by minimizing the approximation error. The estimate of the approximation error of the proposed difference scheme shows that, for small Courant numbers, this scheme whose approximation error is, where the constant c is significantly less than unity, is preferable to use than the original Upwind and Standard Leapfrog schemes whose approximation errors are. The numerical results for the transfer problem based on the proposed scheme are compared with the results obtained using the following schemes: (i) the scheme based on a linear combination of the Standard Leapfrog scheme and the Upwind Leapfrog scheme and (ii) the two-parameter difference scheme of the third order of accuracy.
Keywords: transfer problem, Standard Leapfrog scheme, Upwind Leapfrog scheme, linear weighted combination, increasing of accuracy. 
@article{VMP_2019_20_2_a7,
     author = {A. I. Sukhinov and A. E. Chistyakov and E. A. Protsenko},
     title = {Upwind and {Standard} {Leapfrog} {Difference} {Schemes}},
     journal = {Numerical methods and programming},
     pages = {170--181},
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     number = {2},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2019_20_2_a7/}
}
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A. I. Sukhinov; A. E. Chistyakov; E. A. Protsenko. Upwind and Standard Leapfrog Difference Schemes. Numerical methods and programming, Tome 20 (2019) no. 2, pp. 170-181. http://geodesic.mathdoc.fr/item/VMP_2019_20_2_a7/