Peter Deuflhard Knihy

This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite dimension (algebraic systems) and in infinite dimension (ordinary and partial differential equations). Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. The term 'affine invariance' means that the presented algorithms and their convergence analysis are invariant under one out of four subclasses of affine transformations of the problem to be solved. Compared to traditional textbooks, the distinguishing affine invariance approach leads to shorter theorems and proofs and permits the construction of fully adaptive algorithms. Lots of numerical illustrations, comparison tables, and exercises make the text useful in computational mathematics classes. At the same time, the book opens many directions for possible future research.

This book deals with the general topic “Numerical solution of partial differential equations (PDEs)” with a focus on adaptivity of discretizations in space and time. By and large, introductory textbooks like “Numerical Analysis in Modern Scientific Computing” by Deuflhard and Hohmann should suffice as a prerequisite. The emphasis lies on elliptic and parabolic systems. Hyperbolic conservation laws are treated only on an elementary level excluding turbulence. Numerical Analysis is clearly understood as part of Scientific Computing. The focus is on the efficiency of algorithms, i. e. speed, reliability, and robustness, which directly leads to the concept of adaptivity in algorithms. The theoretical derivation and analysis is kept as elementary as possible. Nevertheless required somewhat more sophisticated mathematical theory is summarized in comprehensive form in an appendix. Complex relations are explained by numerous figures and illustrating examples. Non-trivial problems from regenerative energy, nanotechnology, surgery, and physiology are inserted. The text will appeal to graduate students and researchers on the job in mathematics, science, and technology. Conceptually, it has been written as a textbook including exercises and a software list, but at the same time it should be well-suited for self-study.

This book introduces the main topics of modern numerical analysis: sequence of linear equations, error analysis, least squares, nonlinear systems, symmetric eigenvalue problems, three-term recursions, interpolation and approximation, large systems and numerical integrations. The presentation draws on geometrical intuition wherever appropriate and is supported by a large number of illustrations, exercises, and examples.

Well-known authors; Includes topics and results that have previously not been covered in a book; Uses many interesting examples from science and engineering; Contains numerous homework exercises; Scientific computing is a hot and topical area

On May 21-24, 1997 the Second International Symposium on Algorithms for Macromolecular Modelling was held at the Konrad Zuse Zentrum in Berlin. The event brought together computational scientists in fields like biochemistry, biophysics, physical chemistry, or statistical physics and numerical analysts as well as computer scientists working on the advancement of algorithms, for a total of over 120 participants from 19 countries. In the course of the symposium, the speakers agreed to produce a representative volume that combines survey articles and original papers (all refereed) to give an impression of the present state of the art of Molecular Dynamics.The 29 articles of the book reflect the main topics of the Berlin meeting which were i) Conformational Dynamics, ii) Thermodynamic Modelling, iii) Advanced Time-Stepping Algorithms, iv) Quantum-Classical Simulations and Fast Force Field and v) Fast Force Field Evaluation.

Die Numerische Mathematik bildet einen zentralen Bestandteil der Studiengänge in Mathematik, Ingenieurwissenschaften, Physik und Informatik. Dieses zweibändige Lehrbuch ist speziell für Einführungsvorlesungen konzipiert und bietet eine fundierte Grundlage für weiterführende Studien. Es basiert auf über 30 Jahren Erfahrung des Autors mit Vorlesungsmanuskripten, die an der Friedrich-Schiller-Universität Jena verwendet wurden, und vermittelt praxisnahes Wissen in den Bereichen Numerische Mathematik und Wissenschaftliches Rechnen.

Die numerische Lösung von Anfangs- und Randwertproblemen für gewöhnliche Differentialgleichungen steht im Mittelpunkt dieses Lehrbuchs. Es bietet eine praxisnahe Einführung in bewährte Methoden, die von der theoretischen Herleitung über die Analyse bis zur Implementierung reichen. Zudem werden zahlreiche Anwendungsbeispiele präsentiert, ergänzt durch eine Vielzahl von Übungsaufgaben, die das Verständnis vertiefen und die Anwendung der Methoden fördern.

Die Lehrbuchreihe ist ein Klassiker im deutschsprachigen Raum und behandelt die Numerik von Gleichungssystemen, Interpolation, Integration, Eigenwertproblemen und Differentialgleichungen. Band 3 fokussiert auf partielle Differentialgleichungen und richtet sich an Mathematikstudierende sowie Naturwissenschaftler.