Geodesic
Monotone high-order difference schemes on non-regular grids
Matematičeskoe modelirovanie, Tome 2 (1990) no. 3, pp. 127-149 Cet article a éte moissonné depuis la source Math-Net.Ru

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Paper is devoted to generalization of method for construction monotone high order difference schemes consequently for linear transfer equation, nonlinear transfer equation and for linear system of hyperbolic equations with constant coefficients on «nonregular spatial grid. Schemes are considered of two types. In first type of difference schemes assume that unknown quantities belong to nodes of grid, and in second to the centers of cells. A number of theorems concerning approximation and monotonicity for suggested schemes were proved. Constructed schemes was generalized for equations of ideal gas dynamic, written in Eulerian coordinates. Quality of suggested schemes were proved on numerical example. 
@article{MM_1990_2_3_a11,
     author = {K. V. Vyaznikov},
     title = {Monotone high-order difference schemes on non-regular grids},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {127--149},
     year = {1990},
     volume = {2},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1990_2_3_a11/}
}
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K. V. Vyaznikov. Monotone high-order difference schemes on non-regular grids. Matematičeskoe modelirovanie, Tome 2 (1990) no. 3, pp. 127-149. http://geodesic.mathdoc.fr/item/MM_1990_2_3_a11/