Christian Grossmann, Hans-Görg Roos, Martin Stynes

Numerical Treatment of Partial Differential Equations (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book deals with discretization techniques for elliptic, parabolic and hyperbolic partial differential equations. It provides an introduction to the main principles of discretizations and presents to the reader the ideas and analysis of advanced numerical methods in this area. The book also covers recent research developments - these topics of current interest are rarely considered in other textbooks. It is the authors' aim to give mathematically-inclined students, scientists and engineers a textbook that contains all the basic discretization techniques for the three fundamental types of partial differential equations and in which the reader can find analytical tools, properties of discretizations, and some advice on algorithmic aspects. While finite element methods are the main focus of the book, finite difference methods and finite volume techniques are also presented. Furthermore, the book provides the basic tools needed to solve the discrete problems generated.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 596
• Erscheinungstermin: 11. August 2007
• Englisch
• ISBN-13: 9783540715849
• Artikelnr.: 44127675

Autorenporträt

Christian Grossmann, TU Dresden, Germany / Hans-Görg Roos, TU Dresden, Germany / Martin Stynes, University College Cork, Ireland

Inhaltsangabe

Partial Differential Equations: Basics and Explicit Representation of Solutions.- Finite Difference Methods.- Weak Solutions, Elliptic Problems and Sobolev Spaces.- The Finite Element Method.- Finite Element Methods for Unsteady Problems.- Singular Perturbations.- Numerical Methods for Variational Inequalities and Optimal Control.- Numerical Methods for Discretized Problems.

Rezensionen

From the reviews:

"This textbook is the translation and revision of the third German edition of 2005. ... the book deals with different aspects of the numerical solution of elliptic, parabolic and hyperbolic partial differential equations. ... An index and two pages with a summary of the notations used complete the presentation. ... It can be highly recommended for students and engineers but also for numerical analysts." (Riidiger Weiner, Zentralblatt fiir Angewandte Mathematik and Mechanik, Vol. 88 (12), 2008)