By Sergio Blanes,Fernando Casas
Discover How Geometric Integrators safeguard the most Qualitative houses of constant Dynamical Systems
A Concise creation to Geometric Numerical Integration offers 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 knowing contemporary, complicated study literature on numerical geometric integration.
The booklet first examines high-order classical integration equipment from the constitution protection perspective. It then illustrates the right way to build high-order integrators through the composition of uncomplicated low-order equipment and analyzes the belief of splitting. It subsequent studies symplectic integrators built without delay from the idea of producing capabilities in addition to the real type of variational integrators. The authors additionally clarify the connection among the maintenance of the geometric houses of a numerical process 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 yes sessions of partial differential equations, reminiscent of the Schrödinger equation and different evolution equations.
The motivation of geometric numerical integration is not just to advance numerical equipment with more advantageous qualitative habit but in addition to supply extra exact long-time integration effects than these bought by way of general-purpose algorithms. available to researchers and post-graduate scholars from assorted backgrounds, this introductory publication will get readers up to the mark 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.
Read Online or Download A Concise Introduction to Geometric Numerical Integration (Chapman & Hall/CRC Monographs and Research Notes in Mathematics) PDF
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