Wolfgang Hackbusch Libros

Focusing on the efficiency of multi-grid methods for solving elliptic boundary value problems, this book provides an accessible introduction to multi-grid algorithms alongside a thorough convergence analysis. It includes special applications such as convection-diffusion equations and eigenvalue problems. A detailed presentation of the multi-grid method of the second kind is also featured, highlighting its significance in integral equations and various other issues. Both practical and theoretical readers will find valuable insights within its pages.

Focusing on practical tensor methods, the book explores numerical operations and their applications in various fields, including quantum chemistry, multivariate function approximation, and partial differential equations. It provides a comprehensive guide for understanding and applying these techniques effectively in real-world scenarios.

The second edition offers an in-depth exploration of both classical and modern methods of linear iteration, highlighting the often-overlooked algebraic structure. With the addition of four new chapters and updated references, it provides a comprehensive analysis that enhances understanding of the subject. This edition stands out by focusing on the theoretical underpinnings that are frequently neglected in other works, making it a valuable resource for readers seeking a deeper insight into linear iteration methods.

Focusing on the concept of stability in numerical mathematics, this book provides a comprehensive analysis of its various aspects across different subfields. It offers a comparative framework to characterize stability, making it a valuable resource for understanding how stability is defined and applied in numerical methods.

InhaltsverzeichnisNotation.1 Partielle Differentialgleichungen und ihre Einteilung in Typen.2 Die Potentialgleichung.3 Die Poisson-Gleichung.4 Differenzenmethode für die Poisson-Gleichung.5 Allgemeine Randwertaufgaben.6 Exkurs über Funktionalanalysis.7 Variationsformulierung.8 Die Methode der finiten Elemente.9 Regularität der Lösung.10 Spezielle Differentialgleichungen.11 Eigenwertprobleme.12 Stokes-Gleichungen.