Recent developments in applied mathematics and mechanics: theory, experiment and practice. Devoted to the 80th anniversary of academician N.N.Yanenko

Akademgorodok, Novosibirsk, Russia, June 24 - 29, 2001

Abstracts

Novosibirsk participants

Construction of numerical grids on the basis of a qualitative analysis of singularities

Liseikin V.D., Kitaeva Yu., Likhanova I.

Institute of Computational Technologies (Novosibirsk)

The paper presents some analytical and numerical results concerning possible qualitative structures of solutions to nonlinear singularly perturbed equations wuth singular turning points. The data of the qualitative analysis are used to build coordinate transformations eliminating boundary and interior layers and to formulate appropriate laws of grid distribution in the layers for the purpose of defining uniformly convergent algorithms for the numerical solution of equations with singularities of various types which occur in practical problems. The technique presented is extended to generate adaptive grids implicitly. Examples of grids and numerical experiments with boundary value problems realizing various types of singularities are demonstrated. The paper is supported by the Russian Foundation for the Basic Research (00-01-00900)

Note. Abstracts are published in author's edition

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