By Sergio Blanes,Fernando Casas
Discover How Geometric Integrators defend the most Qualitative houses of continuing Dynamical Systems
A Concise advent to Geometric Numerical Integration offers the most topics, recommendations, and purposes of geometric integrators for researchers in arithmetic, physics, astronomy, and chemistry who're already accustomed to numerical instruments for fixing differential equations. It additionally bargains a bridge from conventional education within the numerical research of differential equations to figuring out contemporary, complicated learn literature on numerical geometric integration.
The e-book first examines high-order classical integration tools from the constitution maintenance standpoint. It then illustrates the way to build high-order integrators through the composition of easy low-order equipment and analyzes the belief of splitting. It subsequent stories symplectic integrators developed without delay from the idea of producing capabilities in addition to the real type of variational integrators. The authors additionally clarify the connection among the protection of the geometric houses of a numerical process and the saw favorable errors propagation in long-time integration. The publication concludes with an research of the applicability of splitting and composition how to sure periods of partial differential equations, akin to the Schrödinger equation and different evolution equations.
The motivation of geometric numerical integration is not just to advance numerical tools with more suitable qualitative habit but additionally to supply extra exact long-time integration effects than these got through general-purpose algorithms. available to researchers and post-graduate scholars from diversified backgrounds, this introductory ebook will get readers up to the mark at the rules, 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 to be had 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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