Информационная система "Конференции"

Abstracts

To solve the Dirichlet problem successfully used high-order scheme. To solve more complex boundary-value problems boundary conditions also must be approximated with adequate accuracy. In this case the methods of pass-through calculation are powerless, as in boundary balanced cells it is not possible to write conservative laws with the necessary exactness. And if it succeeds, they are very cumbersome and inconvenient. To solve the problem while creating high-order difference method it is offered to copy the formulating of problem in the differential form, that is directly to approximated boundary conditions independently from differential equations. To receiving the needed accuracy should apply one-sided multipoint approximation for fluxes. The more points of the grid are used, the higher accuracy is.

Such formulation leads to a problem which is easily reduced to sequence of one-dimensional problems with almost three-diagonal matrix which is obviously possible to solve directly in the ordinary classic way or with application of parallel technologies. We investigated the stability of classical and parallel algorithms in all orders of accuracy.

The proposed method is flexible and has broad application. It successfully can be applied to solve problems with internal boundary conditions in inhomogeneous domains, to solve problems by means of decomposition of complex domains into simple subdomains, as well as to solve problems of interpolation using spline approximation, based on the difference approach.

Work is supported by the Russian fund of Basic Researches, grants № 06-01-00030 and № 08-01-00264.

Note. Abstracts are published in author's edition

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