By Sergio Blanes,Fernando Casas
Discover How Geometric Integrators defend the most Qualitative houses of constant Dynamical Systems
A Concise advent to Geometric Numerical Integration provides the most issues, ideas, and purposes of geometric integrators for researchers in arithmetic, physics, astronomy, and chemistry who're already acquainted with numerical instruments for fixing differential equations. It additionally deals a bridge from conventional education within the numerical research of differential equations to figuring out fresh, complex examine literature on numerical geometric integration.
The e-book first examines high-order classical integration tools from the constitution renovation standpoint. It then illustrates the best way to build high-order integrators through the composition of simple low-order tools and analyzes the belief of splitting. It subsequent reports symplectic integrators built without delay from the speculation of producing capabilities in addition to the real type of variational integrators. The authors additionally clarify the connection among the protection of the geometric houses of a numerical approach and the saw favorable blunders propagation in long-time integration. The publication 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 strengthen numerical tools with more desirable qualitative habit but additionally to supply extra exact long-time integration effects than these bought through general-purpose algorithms. available to researchers and post-graduate scholars from varied backgrounds, this introductory ebook 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 documents 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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