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Informationen zum Autor Shishkin! Grigory I.; Shishkina! Lidia P. Klappentext Grigory Shishkin is well-known for his piecewise uniform meshes method (Shishkin meshes) developed over the last two decades! and the author of a Russian-language research thesis thus far unavailable in English. Difference Methods for Singular Perturbation Problems includes the reference material featured in the Russian original! along with a section containing an overview of recent advances in the field. This volume brings readers up-to-date in numerical and computational methods for analyzing convection-diffusion! boundary element! and fluid dynamics problems where the singular properties of a solution mean that smoothness is limited and therefore traditional methods would not apply. Zusammenfassung Focuses on the development of robust difference schemes for wide classes of boundary value problems. This book explores boundary value problems for elliptic and parabolic reaction-diffusion and convection-diffusion equations in n-dimensional domains with smooth and piecewise-smooth boundaries. Inhaltsverzeichnis Introduction. Boundary Value Problems for Elliptic Reaction-Diffusion Equations in Domains with Smooth Boundaries. Boundary Value Problems for Elliptic Reaction-Diffusion Equations in Domains with Piecewise-Smooth Boundaries. Generalizations for Elliptic Reaction-Diffusion Equations. Parabolic Reaction-Diffusion Equations. Elliptic Convection-Diffusion Equations. Parabolic Convection-Diffusion Equations. Grid Approximations of Parabolic Reaction-Diffusion Equations with Three Perturbation Parameters. Application of Widths for Construction of Difference Schemes for Problems with Moving Boundary Layers. High-Order Accurate Numerical Methods for Singularly Perturbed Problems. A Finite Difference Scheme on a priori Adapted Grids for a Singularly Perturbed Parabolic Convection-Diffusion Equation. On Conditioning of Difference Schemes and Their Matrices for Singularly Perturbed Problems. Approximation of Systems of Singularly Perturbed Elliptic Reaction-Diffusion Equations with Two Parameters. Survey. References. ...
