One- and Two-dimensional bicompact schemes in layered media

Abstract

A new type of difference schemes, i.e., the so-called bicompact schemes, is addressed. Writing such schemes in partial differential equations is reduced to equivalent systems of ordinary differential equations. Spatial derivatives are approximated on a two-point stencil, i.e., within a single grid step. In layered media, in introducing special grids, on which all break points of coefficients are grid nodes, bicompact schemes keep their approximation. Two schemes of the Kochi problem solution for the one-dimensional heat conductivity equation are examined in detail and schemes for two-dimensional problems on arbitrary grids are given.