By Sergio Blanes,Fernando Casas
Discover How Geometric Integrators shield the most Qualitative houses of constant Dynamical Systems
A Concise advent to Geometric Numerical Integration provides the most topics, options, and functions of geometric integrators for researchers in arithmetic, physics, astronomy, and chemistry who're already acquainted with numerical instruments for fixing differential equations. It additionally bargains a bridge from conventional education within the numerical research of differential equations to realizing contemporary, complex study literature on numerical geometric integration.
The publication first examines high-order classical integration equipment from the constitution maintenance perspective. It then illustrates how you can build high-order integrators through the composition of simple low-order equipment 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 upkeep of the geometric houses of a numerical approach and the saw favorable errors propagation in long-time integration. The publication concludes with an research of the applicability of splitting and composition ways to sure sessions of partial differential equations, corresponding to the Schrödinger equation and different evolution equations.
The motivation of geometric numerical integration is not just to boost numerical equipment with more advantageous qualitative habit but additionally to supply extra actual long-time integration effects than these bought by means of general-purpose algorithms. available to researchers and post-graduate scholars from diversified backgrounds, this introductory booklet 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.
Read or Download A Concise Introduction to Geometric Numerical Integration (Chapman & Hall/CRC Monographs and Research Notes in Mathematics) PDF
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A Concise Introduction to Geometric Numerical Integration (Chapman & Hall/CRC Monographs and Research Notes in Mathematics) by Sergio Blanes,Fernando Casas