Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions are the subject of this book. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book...
Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly...
This book presents first-year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculations of practical problems led to infinite series, differential and integral calculus and to differential equations. The establishment of mathematical rigour for these subjects in the 19th century for one and several variables is treated in chapters III and IV. Many quotations are included to give the flavor of the history. The text is complemented by a large number of examples, calculations and mathematical pictures and will provide stimulating...
This book presents first-year calculus roughly in the order in which it was first discovered. The first two chapters show how the ancient calculati...
"Whatever regrets may be, we have done our best." (Sir Ernest Shack- 0 leton, turning back on 9 January 1909 at 88 23' South.) Brahms struggled for 20 years to write his first symphony. Compared to this, the 10 years we have been working on these two volumes may even appear short. This second volume treats stiff differential equations and differential algebraic equations. It contains three chapters: Chapter IV on one-step (Runge-Kutta) meth- ods for stiff problems, Chapter V on multistep methods for stiff problems, and Chapter VI on singular perturbation and differential-algebraic equations....
"Whatever regrets may be, we have done our best." (Sir Ernest Shack- 0 leton, turning back on 9 January 1909 at 88 23' South.) Brahms struggled for 20...
This book deals with methods for solving nonstiff ordinary differential equations. The first chapter describes the historical development of the classical theory, and the second chapter includes a modern treatment of Runge-Kutta and extrapolation methods. Chapter three begins with the classical theory of multistep methods, and concludes with the theory of general linear methods. The reader will benefit from many illustrations, a historical and didactic approach, and computer programs which help him/her learn to solve all kinds of ordinary differential equations. This new edition has been...
This book deals with methods for solving nonstiff ordinary differential equations. The first chapter describes the historical development of the cl...
"Whatever regrets may be, we have done our best." (Sir Ernest Shack- 0 leton, turning back on 9 January 1909 at 88 23' South.) Brahms struggled for 20 years to write his first symphony. Compared to this, the 10 years we have been working on these two volumes may even appear short. This second volume treats stiff differential equations and differential algebraic equations. It contains three chapters: Chapter IV on one-step (Runge-Kutta) meth- ods for stiff problems, Chapter V on multistep methods for stiff problems, and Chapter VI on singular perturbation and differential-algebraic equations....
"Whatever regrets may be, we have done our best." (Sir Ernest Shack- 0 leton, turning back on 9 January 1909 at 88 23' South.) Brahms struggled for 20...
Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions are the subject of this book. A complete self-contained theory of symplectic and symmetric methods, which include Runge-Kutta, composition, splitting, multistep and various specially designed integrators, is presented and their construction and practical merits are discussed. The long-time behaviour of the numerical solutions is studied using a backward error analysis (modified equations) combined with KAM theory. The book...
Numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly...
This book deals with methods for solving nonstiff ordinary differential equations. The first chapter describes the historical development of the classical theory, and the second chapter includes a modern treatment of Runge-Kutta and extrapolation methods. Chapter three begins with the classical theory of multistep methods, and concludes with the theory of general linear methods. The reader will benefit from many illustrations, a historical and didactic approach, and computer programs which help him/her learn to solve all kinds of ordinary differential equations. This new edition has been...
This book deals with methods for solving nonstiff ordinary differential equations. The first chapter describes the historical development of the cl...
Diese Einfuhrung in die Analysis orientiert sich an der historischen Entwicklung: Die ersten zwei Kapitel schlagen den Bogen von historischen Berechnungsmethoden zu unendlichen Reihen, zur Differential- und Integralrechnung und zu Differentialgleichungen. Die Etablierung einer mathematisch stringenten Denkhaltung im 19. Jahrhundert fur ein und mehrere Variablen ist Thema der darauffolgenden Kapitel. Viele Beispiele, Berechnungen und Bilder machen den Band zu einem Lesevergnugen fur Studierende, fur Lehrer und fur Wissenschaftler."
Diese Einfuhrung in die Analysis orientiert sich an der historischen Entwicklung: Die ersten zwei Kapitel schlagen den Bogen von historischen Berechnu...
In this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the ancient Greeks established geometry, together with its numerous practical applications, while more recent findings on Euclidian geometry are discussed as well. The following three chapters explain the revolution in geometry due to the progress made in the field of algebra by Descartes, Euler and Gauss. Spatial geometry, vector algebra and matrices are treated in chapters 9 and 10. The last chapter offers an introduction to projective geometry, which...
In this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the anci...
Dieses Buch fuhrt Sie in die Programmierung verteilter Systeme in Java ein. Besonderer Wert wird auf die Realisierung serverseitiger Anwendungen im Rahmen der Java EE-Architektur gelegt. Schritt fur Schritt lernen Sie alle wichtigen Technologien und Bestandteile von Enterprise Java sowie deren Zusammenspiel kennen.
Jedes Kapitel enthalt zahlreiche Beispiele und Ubungsaufgaben, sodass der Leser nach der Lekture des Buches in der Lage ist, komponentenbasierte Webanwendungen auf Basis der Java Enterprise-Architektur zu erstellen.
Alle Ubungen inklusive Losungen sowie die...
Dieses Buch fuhrt Sie in die Programmierung verteilter Systeme in Java ein. Besonderer Wert wird auf die Realisierung serverseitiger Anwendungen im...
