By Sergio Blanes,Fernando Casas
Discover How Geometric Integrators guard the most Qualitative homes of constant Dynamical Systems
A Concise creation to Geometric Numerical Integration offers the most issues, ideas, and purposes of geometric integrators for researchers in arithmetic, physics, astronomy, and chemistry who're already acquainted with numerical instruments for fixing differential equations. It additionally deals a bridge from conventional education within the numerical research of differential equations to figuring out fresh, complicated study literature on numerical geometric integration.
The e-book first examines high-order classical integration tools from the constitution maintenance perspective. It then illustrates the best way to build high-order integrators through the composition of uncomplicated low-order tools and analyzes the belief of splitting. It subsequent reports symplectic integrators built at once from the idea of producing features in addition to the real type of variational integrators. The authors additionally clarify the connection among the upkeep of the geometric houses of a numerical process and the saw favorable blunders propagation in long-time integration. The e-book concludes with an research of the applicability of splitting and composition how to yes periods of partial differential equations, corresponding to the Schrödinger equation and different evolution equations.
The motivation of geometric numerical integration isn't just to improve numerical equipment with enhanced qualitative habit but additionally to supply extra exact long-time integration effects than these acquired through general-purpose algorithms. obtainable to researchers and post-graduate scholars from various backgrounds, this introductory booklet will get readers on top of things at the principles, equipment, and functions of this box. Readers can reproduce the figures and effects given within the textual content utilizing the MATLAB® courses and version documents on hand online.
Read or Download A Concise Introduction to Geometric Numerical Integration (Chapman & Hall/CRC Monographs and Research Notes in Mathematics) PDF
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Extra resources for A Concise Introduction to Geometric Numerical Integration (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)
A Concise Introduction to Geometric Numerical Integration (Chapman & Hall/CRC Monographs and Research Notes in Mathematics) by Sergio Blanes,Fernando Casas