A Concise Introduction to Geometric Numerical Integration

Nonfiction, Science & Nature, Mathematics, Number Systems, Differential Equations, Arithmetic
Cover of the book A Concise Introduction to Geometric Numerical Integration by Sergio Blanes, Fernando Casas, CRC Press
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Sergio Blanes, Fernando Casas ISBN: 9781315354866
Publisher: CRC Press Publication: November 22, 2017
Imprint: Chapman and Hall/CRC Language: English
Author: Sergio Blanes, Fernando Casas
ISBN: 9781315354866
Publisher: CRC Press
Publication: November 22, 2017
Imprint: Chapman and Hall/CRC
Language: English

Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous Dynamical Systems

A Concise Introduction to Geometric Numerical Integration presents the main themes, techniques, and applications of geometric integrators for researchers in mathematics, physics, astronomy, and chemistry who are already familiar with numerical tools for solving differential equations. It also offers a bridge from traditional training in the numerical analysis of differential equations to understanding recent, advanced research literature on numerical geometric integration.

The book first examines high-order classical integration methods from the structure preservation point of view. It then illustrates how to construct high-order integrators via the composition of basic low-order methods and analyzes the idea of splitting. It next reviews symplectic integrators constructed directly from the theory of generating functions as well as the important category of variational integrators. The authors also explain the relationship between the preservation of the geometric properties of a numerical method and the observed favorable error propagation in long-time integration. The book concludes with an analysis of the applicability of splitting and composition methods to certain classes of partial differential equations, such as the Schrödinger equation and other evolution equations.

The motivation of geometric numerical integration is not only to develop numerical methods with improved qualitative behavior but also to provide more accurate long-time integration results than those obtained by general-purpose algorithms. Accessible to researchers and post-graduate students from diverse backgrounds, this introductory book gets readers up to speed on the ideas, methods, and applications of this field. Readers can reproduce the figures and results given in the text using the MATLAB® programs and model files available online.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

Discover How Geometric Integrators Preserve the Main Qualitative Properties of Continuous Dynamical Systems

A Concise Introduction to Geometric Numerical Integration presents the main themes, techniques, and applications of geometric integrators for researchers in mathematics, physics, astronomy, and chemistry who are already familiar with numerical tools for solving differential equations. It also offers a bridge from traditional training in the numerical analysis of differential equations to understanding recent, advanced research literature on numerical geometric integration.

The book first examines high-order classical integration methods from the structure preservation point of view. It then illustrates how to construct high-order integrators via the composition of basic low-order methods and analyzes the idea of splitting. It next reviews symplectic integrators constructed directly from the theory of generating functions as well as the important category of variational integrators. The authors also explain the relationship between the preservation of the geometric properties of a numerical method and the observed favorable error propagation in long-time integration. The book concludes with an analysis of the applicability of splitting and composition methods to certain classes of partial differential equations, such as the Schrödinger equation and other evolution equations.

The motivation of geometric numerical integration is not only to develop numerical methods with improved qualitative behavior but also to provide more accurate long-time integration results than those obtained by general-purpose algorithms. Accessible to researchers and post-graduate students from diverse backgrounds, this introductory book gets readers up to speed on the ideas, methods, and applications of this field. Readers can reproduce the figures and results given in the text using the MATLAB® programs and model files available online.

More books from CRC Press

Cover of the book What Makes a Good Healthcare System? by Sergio Blanes, Fernando Casas
Cover of the book Engineering Electrodynamics by Sergio Blanes, Fernando Casas
Cover of the book Animation: A World History by Sergio Blanes, Fernando Casas
Cover of the book Hepatitis A by Sergio Blanes, Fernando Casas
Cover of the book Pre-Accident Investigations by Sergio Blanes, Fernando Casas
Cover of the book GPs and Purchasing in the NHS: The Internal Market and Beyond by Sergio Blanes, Fernando Casas
Cover of the book Structural Analysis of Laminated Anisotropic Plates by Sergio Blanes, Fernando Casas
Cover of the book Claims, Disputes and Litigation Involving BIM by Sergio Blanes, Fernando Casas
Cover of the book Smart Sensors for Industrial Applications by Sergio Blanes, Fernando Casas
Cover of the book Flexible Network Architectures Security by Sergio Blanes, Fernando Casas
Cover of the book Psychiatric Presentations in General Practice by Sergio Blanes, Fernando Casas
Cover of the book Probiotics in Mental Health by Sergio Blanes, Fernando Casas
Cover of the book Advances in Particle Therapy by Sergio Blanes, Fernando Casas
Cover of the book Patients, the Public and Priorities in Healthcare by Sergio Blanes, Fernando Casas
Cover of the book Structural Analysis by Sergio Blanes, Fernando Casas
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy