By Sergio Blanes,Fernando Casas
Discover How Geometric Integrators look after the most Qualitative houses of continuing Dynamical Systems
A Concise advent to Geometric Numerical Integration provides the most issues, concepts, and functions of geometric integrators for researchers in arithmetic, physics, astronomy, and chemistry who're already acquainted with numerical instruments for fixing differential equations. It additionally bargains a bridge from conventional education within the numerical research of differential equations to knowing fresh, complicated learn literature on numerical geometric integration.
The ebook first examines high-order classical integration equipment from the constitution protection perspective. It then illustrates tips on how to build high-order integrators through the composition of easy low-order tools and analyzes the belief of splitting. It subsequent studies symplectic integrators built without delay from the speculation of producing capabilities in addition to the real classification of variational integrators. The authors additionally clarify the connection among the protection of the geometric homes of a numerical approach and the saw favorable mistakes propagation in long-time integration. The e-book concludes with an research of the applicability of splitting and composition tips on how to sure sessions of partial differential equations, equivalent to the Schrödinger equation and different evolution equations.
The motivation of geometric numerical integration isn't just to improve numerical tools with better qualitative habit but additionally to supply extra actual long-time integration effects than these bought by way of general-purpose algorithms. available to researchers and post-graduate scholars from different backgrounds, this introductory publication will get readers on top of things at the principles, equipment, and purposes of this box. Readers can reproduce the figures and effects given within the textual content utilizing the MATLAB® courses and version records to be had online.
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Additional info 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