This article is cited in 1 paper

On compact approximations of divergent differential equations

V. V. Ostapenko<sup>ab

a</sup> Lavrent'ev Institute of Hydrodynamics, Novosibirsk
^b Novosibirsk State University, Novosibirsk

Abstract: The method for construction of compact difference schemes approximating the divergent differential equations is proposed. The schemes have an arbitrary order of approximation on a stencil of a common type. It is shown that construction of such schemes for partial differential equations is based on spatial compact schemes approximating ordinary differential equations depending on several independent functions. Necessary and sufficient conditions on factors of these schemes, at which they have a high order of approximation, are obtained. Examples of restoration with these schemes of compact difference schemes for partial differential equations are given. It is shown that such compact difference schemes have the same order as classical approximation on smooth solutions and weak approximations on discontinuous solutions.

Key words: divergent differential equations, compact difference schemes, high order of approximation.

UDC: 519.63

Received: 21.03.2011
Revised: 25.06.2011

 English version: Numerical Analysis and Applications, 2012, 5:3, 242–253

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