Shishkin / Shishkina Difference Methods for Singular Perturbation Problems

Erscheinungsjahr 2010
ISBN: 978-0-203-49241-3
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 408 Seiten

Reihe: Monographs and Surveys in Pure and Applied Mathematics

Difference Methods for Singular Perturbation Problems focuses on the development of robust difference schemes for wide classes of boundary value problems. It justifies the e-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 e 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 e uniformly convergent finite difference schemes for broad classes of singularly perturbed boundary value problems.

Zielgruppe

Numerical analysts, mathematical physicists and engineers, and graduate students and researchers in fluid dynamics and numerical mathematics.

Autoren/Hrsg.

Shishkin, Grigory I.

Shishkina, Lidia P.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

Preface
Part I: Grid Approximations of Singular Perturbation Partial Differential Equations
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
Part II: Advanced Trends in e Uniformly Convergent Difference Methods
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