Geodesic
1D and 2D bicompact schemes in layered mediums
Matematičeskoe modelirovanie, Tome 21 (2009) no. 8, pp. 44-62.

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New type of differential schemes – so called bicompact schemes was considered. To derive such schemes we transform PDE into system of PDEs. Spatial derivatives are approximated on 2-points stencil, i.e. within single grid step. In layered mediums bicompact schemes keep their approximation if we set a special grid in a way that all points where coefficients have breaks are nodes of the grid. Two schemes for 1-dimensional hyperbolic problem were considered in details and schemes for 2D problems are given. 
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N. N. Kalitkin; P. V. Koryakin. 1D and 2D bicompact schemes in layered mediums. Matematičeskoe modelirovanie, Tome 21 (2009) no. 8, pp. 44-62. http://geodesic.mathdoc.fr/item/MM_2009_21_8_a4/

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