Geodesic
Difference scheme of high order consistency for transfere equation
Matematičeskoe modelirovanie, Tome 6 (1994) no. 2, pp. 113-122.

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The method of TVD-type difference scheme constructing is proposed. The obtained scheme is used for numerical solving of transport equation and it is constructed by adding antidiffusional fluxes to initial first order scheme. The scheme has a simple form. It is explicit, conservative and third order of consistency in the field of smooth solutions (except vicinities of extremums on the uniform spatial grid). The simple algorithm for difference equation decision in the case of two spatial variables is proposed. It allows to conserve the scheme consistency order for commutative spatial operators. 
@article{MM_1994_6_2_a9,
     author = {E. V. Dyankova and O. S. Shirokovskaya},
     title = {Difference scheme of high order consistency for transfere equation},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {113--122},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1994_6_2_a9/}
}
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E. V. Dyankova; O. S. Shirokovskaya. Difference scheme of high order consistency for transfere equation. Matematičeskoe modelirovanie, Tome 6 (1994) no. 2, pp. 113-122. http://geodesic.mathdoc.fr/item/MM_1994_6_2_a9/