By Sergio Blanes,Fernando Casas
Discover How Geometric Integrators guard the most Qualitative homes of continuing Dynamical Systems
A Concise creation to Geometric Numerical Integration offers the most topics, innovations, 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 knowing fresh, complex learn literature on numerical geometric integration.
The e-book first examines high-order classical integration equipment from the constitution protection perspective. It then illustrates easy methods to build high-order integrators through the composition of easy low-order tools and analyzes the belief of splitting. It subsequent experiences symplectic integrators built without delay from the speculation of producing features in addition to the real classification of variational integrators. The authors additionally clarify the connection among the upkeep of the geometric homes of a numerical approach and the saw favorable errors propagation in long-time integration. The ebook concludes with an research of the applicability of splitting and composition easy methods to definite sessions of partial differential equations, reminiscent of the Schrödinger equation and different evolution equations.
The motivation of geometric numerical integration is not just to enhance numerical equipment with stronger qualitative habit but in addition to supply extra actual long-time integration effects than these acquired by way of general-purpose algorithms. available to researchers and post-graduate scholars from diversified backgrounds, this introductory ebook will get readers in control 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 records to be had 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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Extra 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