Geodesic
To justification of the integral convergence method for studying the finite-difference schemes accuracy
Matematičeskoe modelirovanie, Tome 33 (2021) no. 4, pp. 45-59

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We justified the method of integral convergence for studying the accuracy of finitedifference shock-capturing schemes for numerical simulation of shock waves propagating at a variable speed. The order of integral convergence is determined using a series of numerical calculations on a family of embedded difference grids. It allows us to model a space-continuous difference solution of the corresponding Cauchy problem. This approach is used to study the accuracy of explicit finite-difference schemes such as Rusanov scheme, TVD and WENO schemes, which have a higher order of classic approximation, as well as an implicit compact scheme with artificial viscosity of the fourth order of divergence, which has a third order of both classic and weak approximation.
Keywords: intergal convergence of difference schemes, Rusanov scheme, TVD scheme, WENO scheme, compact scheme. 
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     author = {V. V. Ostapenko and N. A. Khandeeva},
     title = {To justification of the integral convergence method for studying the finite-difference schemes accuracy},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {45--59},
     publisher = {mathdoc},
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     number = {4},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2021_33_4_a2/}
}
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V. V. Ostapenko; N. A. Khandeeva. To justification of the integral convergence method for studying the finite-difference schemes accuracy. Matematičeskoe modelirovanie, Tome 33 (2021) no. 4, pp. 45-59. http://geodesic.mathdoc.fr/item/MM_2021_33_4_a2/