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, thoughts, and purposes of geometric integrators for researchers in arithmetic, physics, astronomy, and chemistry who're already conversant in numerical instruments for fixing differential equations. It additionally bargains a bridge from conventional education within the numerical research of differential equations to realizing fresh, complex examine literature on numerical geometric integration.
The publication first examines high-order classical integration tools from the constitution upkeep viewpoint. It then illustrates find out how to build high-order integrators through the composition of uncomplicated low-order equipment and analyzes the belief of splitting. It subsequent studies symplectic integrators developed at once from the idea of producing features in addition to the real classification of variational integrators. The authors additionally clarify the connection among the protection of the geometric houses of a numerical technique and the saw favorable blunders propagation in long-time integration. The ebook concludes with an research of the applicability of splitting and composition how you can sure periods of partial differential equations, equivalent to the Schrödinger equation and different evolution equations.
The motivation of geometric numerical integration isn't just to improve numerical equipment with greater qualitative habit but additionally to supply extra actual long-time integration effects than these got via general-purpose algorithms. available to researchers and post-graduate scholars from various backgrounds, this introductory e-book will get readers in control at the principles, tools, and purposes 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.
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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