By Sergio Blanes,Fernando Casas
Discover How Geometric Integrators guard the most Qualitative homes of continuing Dynamical Systems
A Concise advent to Geometric Numerical Integration provides the most subject matters, options, and functions of geometric integrators for researchers in arithmetic, physics, astronomy, and chemistry who're already conversant in 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 learn literature on numerical geometric integration.
The e-book first examines high-order classical integration equipment from the constitution upkeep viewpoint. It then illustrates the way to build high-order integrators through the composition of uncomplicated low-order tools and analyzes the assumption of splitting. It subsequent experiences symplectic integrators developed without delay from the idea of producing features in addition to the $64000 class of variational integrators. The authors additionally clarify the connection among the upkeep 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 how you can definite periods of partial differential equations, reminiscent of the Schrödinger equation and different evolution equations.
The motivation of geometric numerical integration isn't just to enhance numerical tools with superior qualitative habit but additionally to supply extra actual long-time integration effects than these received via general-purpose algorithms. obtainable to researchers and post-graduate scholars from assorted backgrounds, this introductory booklet will get readers up to the mark 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 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