Институт вычислительной математики и математической геофизики СОРАН

Abstracts

numerical solution of DE and IE

The report generalizes the universal technology of calculation of boundary problems in piecewise homogeneous domains, earlier developed by the author for second order equations in Cartesian coordinates, to an arbitrary orthogonal coordinate system. The technique is applicable for both ordinary schemes of second-order approximation, and for the compact schemes of fourth order. It also allow in addition to the usual well as the parallel realization.

The essence of technology is that within the homogeneous parts of the area used by the classical scheme of second to fourth order accuracy, and at internal boundaries the flow continuity conditions are approximated directly using multipoint one-sided difference analogues of the first derivatives. External boundary conditions are approximated by same way.

In order closure algorithm developed special formulas for computing the desired function at the grid nodes, which correspond to the corners of homogeneous subdomains. These formulas, as earlier to the Cartesian coordinates, constructed in general form with arbitrary order of accuracy.

Note. Abstracts are published in author's edition

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