By Sergio Blanes,Fernando Casas
Discover How Geometric Integrators shield the most Qualitative houses of continuing Dynamical Systems
A Concise creation to Geometric Numerical Integration provides the most issues, thoughts, 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 deals a bridge from conventional education within the numerical research of differential equations to knowing contemporary, complicated learn literature on numerical geometric integration.
The e-book first examines high-order classical integration equipment from the constitution upkeep perspective. It then illustrates easy methods to build high-order integrators through the composition of uncomplicated low-order tools and analyzes the assumption of splitting. It subsequent reports symplectic integrators built at once from the speculation of producing capabilities in addition to the real class of variational integrators. The authors additionally clarify the connection among the protection of the geometric homes of a numerical technique and the saw favorable mistakes propagation in long-time integration. The ebook concludes with an research of the applicability of splitting and composition the way to convinced sessions of partial differential equations, comparable to the Schrödinger equation and different evolution equations.
The motivation of geometric numerical integration is not just to advance numerical tools with better qualitative habit but in addition to supply extra actual long-time integration effects than these bought via general-purpose algorithms. available to researchers and post-graduate scholars from assorted backgrounds, this introductory ebook will get readers in control 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 records on hand online.
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Extra 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