By Sergio Blanes,Fernando Casas
Discover How Geometric Integrators shield the most Qualitative homes of constant Dynamical Systems
A Concise creation to Geometric Numerical Integration offers the most topics, ideas, and functions 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 realizing fresh, complicated examine literature on numerical geometric integration.
The ebook first examines high-order classical integration equipment from the constitution upkeep perspective. It then illustrates tips on how to build high-order integrators through the composition of uncomplicated low-order equipment and analyzes the belief of splitting. It subsequent reports symplectic integrators developed without delay from the idea of producing capabilities in addition to the real class of variational integrators. The authors additionally clarify the connection among the protection of the geometric houses of a numerical process and the saw favorable mistakes propagation in long-time integration. The ebook concludes with an research of the applicability of splitting and composition ways to 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 boost numerical tools with more desirable qualitative habit but in addition to supply extra actual long-time integration effects than these bought by means of general-purpose algorithms. obtainable to researchers and post-graduate scholars from varied backgrounds, this introductory publication will get readers in control at the rules, 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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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