Difference Methods for Singular Perturbation Problems

Grigory I. Shishkin

ISBN 10: 1584884592 / ISBN 13: 9781584884590

Published by Taylor & Francis Inc Sep 2008, 2008

About this Item

Neuware - 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.

Seller Inventory # 9781584884590

Bibliographic Details

• Title: Difference Methods for Singular Perturbation Problems
• Publisher: Taylor & Francis Inc Sep 2008
• Publication Date: 2008
• Language: English
• ISBN 10: 1584884592
• ISBN 13: 9781584884590
• Binding: Buch
• Condition: Neu
• Dimensions: 240W x 163H x 25D millimeters 240 millimeters width by 163 millimeters height by 25 millimeters depth
• Weight: 694 grams

About this title

Synopsis

Difference Methods for Singular Perturbation Problems focuses on the development of robust difference schemes for wide classes of boundary value problems. It justifies the ε-uniform convergence of these schemes and surveys the latest approaches important for further progress in numerical methods.

The first part of the 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. The authors develop a technique for constructing and justifying ε uniformly convergent difference schemes for boundary value problems with fewer restrictions on the problem data.

Containing information published mainly in the last four years, the second section focuses on problems with boundary layers and additional singularities generated by nonsmooth data, unboundedness of the domain, and the perturbation vector parameter. This part also studies both the solution and its derivatives with errors that are independent of the perturbation parameters.

Co-authored by the creator of the Shishkin mesh, this book presents a systematic, detailed development of approaches to construct ε uniformly convergent finite difference schemes for broad classes of singularly perturbed boundary value problems.

About the Author

Shishkin, Grigory I.; Shishkina, Lidia P.