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 provides the most issues, suggestions, 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 study literature on numerical geometric integration.
The publication first examines high-order classical integration equipment from the constitution upkeep viewpoint. It then illustrates tips to build high-order integrators through the composition of simple low-order tools and analyzes the belief of splitting. It subsequent experiences symplectic integrators built without delay from the idea of producing features in addition to the real classification of variational integrators. The authors additionally clarify the connection among the protection of the geometric houses of a numerical procedure and the saw favorable blunders propagation in long-time integration. The e-book concludes with an research of the applicability of splitting and composition ways to convinced periods of partial differential equations, equivalent to the Schrödinger equation and different evolution equations.
The motivation of geometric numerical integration is not just to strengthen numerical tools with superior qualitative habit but in addition to supply extra exact long-time integration effects than these got via general-purpose algorithms. obtainable to researchers and post-graduate scholars from different backgrounds, this introductory booklet will get readers up to the mark at the principles, tools, and purposes 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.
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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