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Springer Geometric Numerical Integration - Mathematics Book

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Description

Explore advanced mathematical methods with Geometric Numerical Integration by Springer. This volume, part of the Springer Series in Computational Mathematics, focuses on numerical methods that preserve the essential properties of Hamiltonian systems, reversible systems, and differential equations on manifolds. It provides a comprehensive look at problems involving highly oscillatory solutions. Readers will find a self-contained theory covering symplectic and symmetric methods. The text details the construction and practical merits of various integrators, including Runge-Kutta, composition, splitting, multistep, and other specially designed methods. To understand long-time behavior, the book utilizes backward error analysis through modified equations combined with KAM theory. This text is an essential resource for those studying structure-preserving algorithms for ordinary differential equations. Whether you are researching computational mathematics or applied physics, this book offers the theoretical depth and practical discussion needed to master complex numerical integration techniques.

Key Features

Comprehensive theory of symplectic and symmetric methods including Runge-Kutta and splitting integrators.

Detailed analysis of numerical methods for Hamiltonian and reversible systems.

In-depth study of long-time behavior using backward error analysis and KAM theory.

Covers specialized solutions for differential equations on manifolds and oscillatory problems.

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Product Specifications

Format
paperback
Domain
Amazon UK
Release Date
11 March 2010
Listed Since
23 September 2009

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