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Ernst Hairer

    19. Juni 1949
    Geometric numerical integration
    Geometric Numerical Integration
    Analysis in historischer Entwicklung
    • Analysis in historischer Entwicklung

      • 405 Seiten
      • 15 Lesestunden
      4,4(11)Abgeben

      Diese Einführung 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 für ein und mehrere Variablen ist Thema der darauffolgenden Kapitel. Viele Beispiele, Berechnungen und Bilder machen den Band zu einem Lesevergnügen – für Studierende, für Lehrer und für Wissenschaftler.

      Analysis in historischer Entwicklung
    • Geometric Numerical Integration

      Structure-Preserving Algorithms for Ordinary Differential Equations

      • 644 Seiten
      • 23 Lesestunden
      5,0(1)Abgeben

      The book offers a distinctive approach to KAM theory through a numerical perspective, setting it apart from other texts in the field. It delves into the intricacies of this mathematical theory, providing insights and methodologies that are not commonly found in existing literature. This focus on numerical analysis makes it a valuable resource for those looking to deepen their understanding of KAM theory.

      Geometric Numerical Integration
    • Geometric numerical integration

      Structure preserving algorithms for ordinary differential equations

      • 528 Seiten
      • 19 Lesestunden
      4,2(7)Abgeben

      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 is illustrated by many figures, it treats applications from physics and astronomy and contains many numerical experiments and comparisons of different approaches.

      Geometric numerical integration