This text provides an introduction to the numerical solution of initial and boundary value problems in ordinary differential equations on a firm theoretical basis. The book strictly presents numerical analysis as part of the more general field of scientific computing. Important algorithmic concepts are explained down to questions of software implementation. For initial value problems a dynamical systems approach is used to develop Runge-Kutta, extrapolation, and multistep methods. For boundary value problems including optimal control problems both multiple shooting and collocation methods are worked out in detail. Graduate students and researchers in mathematics, computer science, and engineering will find this book useful. Chapter summaries, detailed illustrations, and exercises are contained throughout the book with many interesting applications taken from a rich variety of areas.Peter Deuflhard is founder and president of the Zuse Institute Berlin (ZIB) and full professor of scientific computing at the Free University of Berlin, department of mathematics and computer science.Folkmar Bornemann is full professor of scientific computing at the Center of Mathematical Sciences, Technical University of Munich.

This introductory book directs the reader to a selection of useful elementary numerical algorithms on a reasonably sound theoretical basis, built up within the text. The primary aim is to develop algorithmic thinking -- emphasizing long living computational concepts over fast changing software issues. The guiding principle is to explain modern numerical analysis concepts applicable in complex scientific computing at much simpler model problems. For example, the two adaptive techniques in numerical quadrature elaborated here carry the germs for either extrapolation methods or multigrid methods in differential equations, which are not treated here. The presentation draws on geometrical intuition wherever appropriate, supported by a large number of illustrations. Numerous exercises are included for further practice and improved understanding. This text will appeal to undergraduate and graduate students as well as researchers in mathematics, computer science, science, and engineering. At the same time it is addressed to practical computational scientists who, via self-study, wish to become acquainted with modern concepts of numerical analysis and scientific computing on an elementary level. Sole prerequisite is undergraduate knowledge in Linear Algebra and Calculus.

This book is intended for students of computational systems biology with only a limited background in mathematics. Typical books on systems biology merely mention algorithmic approaches, but without offering a deeper understanding. On the other hand, mathematical books are typically unreadable for computational biologists. The authors of the present book have worked hard to fill this gap. The result is not a book on systems biology, but on computational methods in systems biology. This book originated from courses taught by the authors at Freie Universitat Berlin. The guiding idea of the courses was to convey those mathematical insights that are indispensable for systems biology, teaching the necessary mathematical prerequisites by means of many illustrative examples and without any theorems. The three chapters cover the mathematical modelling of biochemical and physiological processes, numerical simulation of the dynamics of biological networks and identification of model parameters by means of comparisons with real data. Throughout the text, the strengths and weaknesses of numerical algorithms with respect to various systems biological issues are discussed. Web addresses for downloading the corresponding software are also included.

This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite and in infinite dimension. Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems. 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 is intended for students of computational systems biology with only a limited background in mathematics. Typical books on systems biology merely mention algorithmic approaches, but without offering a deeper understanding. On the other hand, mathematical books are typically unreadable for computational biologists. The authors of the present book have worked hard to fill this gap. The result is not a book on systems biology, but on computational methods in systems biology. This book originated from courses taught by the authors at Freie Universität Berlin. The guiding idea of the courses was to convey those mathematical insights that are indispensable for systems biology, teaching the necessary mathematical prerequisites by means of many illustrative examples and without any theorems. The three chapters cover the mathematical modelling of biochemical and physiological processes, numerical simulation of the dynamics of biological networks and identification of model parameters by means of comparisons with real data. Throughout the text, the strengths and weaknesses of numerical algorithms with respect to various systems biological issues are discussed. Web addresses for downloading the corresponding software are also included.

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 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.

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

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.

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.

Praktiken visueller Welterzeugung in Form von Weltbildern lassen sich bereits in der Antike beobachten und haben sich bis heute als Mittel zur Konstruktion von Ordnungsvorstellungen bewahrt. Seit jeher steht der begrifflichen Ordnung der Welt eine modellhaft anschauliche Ordnung gegenuber. Die grundlegende Bedeutung, die Anschaulichkeit fur unser Verstandnis von der Welt spielt und die die vielfaltigsten Weltbilder hervorgebracht hat, ist jedoch mehr als eine blosse Wiederholung des Sehens. Die Bildwelten der Weltbilder geben uns nicht nur ein anschauliches Bild von der Welt und vom Kosmos. Sie sind zugleich wirkungsmachtige Instrumente zum praktischen und theoretischen Handeln in der Welt und formen auf unterschiedlichste Weise unsere Vorstellungen von der Welt und unsere Weltanschauung. Die grundlegenden Fragen, die dabei gestellt werden, haben sich durch die Jahrhunderte nicht wirklich geandert. Sie betreffen die den Menschen umfassende Ordnung und seine Stellung innerhalb dieser Ordnung: Welche Gestalt hat die Welt? Welche Krafte und Ideen wirken in ihr? Woraus besteht sie? Wie ist sie entstanden? Wie sieht ihre Zukunft aus? Bereits die fruhen Beispiele von Weltbildern machen deutlich, dass die sowohl in Bildern als auch in Erzahlungen zur Erscheinung gebrachte Wirklichkeit immer eine vom Menschen hervorgebrachte ist und daher stets interpretierte Wirklichkeit und symbolische Konstruktion bedeutet. Die gesammelten Beispiele reprasentieren zugleich unterschiedliche visuelle Medien, die im Dienst der Konstruktion der Welt als Bild stehen. Damit ist die Geschichte der Weltbilder nicht nur eine Geschichte wechselnder Weltvorstellungen, sondern zugleich auch eine Geschichte wechselnder Darstellungsmethoden und unterschiedlicher Tragermedien. Der Atlas der Weltbilder behandelt ein breites Spektrum von Artefakten und schreitet einen grossen zeitlichen Bogen ab, der mit altorientalischen und altagyptischen Weltkonzeptionen beginnt und mit aktuellen Simulationen der Astrophysik endet. Der Atlas der Weltbilder dokumentiert somit Aspekte der Kulturgeschichte visueller Welterzeugung in Form von Weltbildern aus den zuruckliegenden zweieinhalb Jahrtausenden. Paradigmatische Analysen der Prinzipien und Funktionen sowie der Geschichte und Bedeutung von Weltbildern geben erstmals umfassenden Aufschluss uber dieses umfangreiche Themengebiet."

This textbook deals with the numerical solution of initial and boundary value problems for ordinary differential equations. It takes the reader directly to the practically proven methods - from their theoretical foundation via their analysis to questions of implementation. The textbook contains a wealth of exercises together with numerous application examples. Sections of this third edition have been revised and it has been supplemented with MATLAB codes.

This is Volume 2 of the 4th revised and expanded edition of this standard work on numerical approaches to ordinary differential equations. It describes processes for numerically solving basic and boundary value problems for ordinary differential equations. The text guides the reader through tried and true practical methods, and includes numerous examples of the use of ordinary differential equations.