Download Algorithmic Lie Theory for Solving Ordinary Differential by Fritz Schwarz PDF

By Fritz Schwarz

even though Sophus Lie's idea used to be nearly the one systematic process for fixing nonlinear usual differential equations (ODEs), it was once not often used for useful difficulties due to the colossal quantity of calculations concerned. yet with the appearance of laptop algebra courses, it turned attainable to use Lie idea to concrete difficulties. Taking this strategy, Algorithmic Lie thought for fixing traditional Differential Equations serves as a precious advent for fixing differential equations utilizing Lie's concept and similar results.

After an introductory bankruptcy, the publication presents the mathematical starting place of linear differential equations, overlaying Loewy's concept and Janet bases. the subsequent chapters current effects from the idea of continuing teams of a 2-D manifold and speak about the shut relation among Lie's symmetry research and the equivalence challenge. The middle chapters of the booklet establish the symmetry sessions to which quasilinear equations of order or 3 belong and remodel those equations to canonical shape. the ultimate chapters resolve the canonical equations and convey the overall ideas at any time when attainable in addition to supply concluding comments. The appendices comprise suggestions to chose routines, invaluable formulae, houses of beliefs of monomials, Loewy decompositions, symmetries for equations from Kamke's assortment, and a short description of the software program method ALLTYPES for fixing concrete algebraic problems.

Show description

Read Online or Download Algorithmic Lie Theory for Solving Ordinary Differential Equations (Chapman & Hall/CRC Pure and Applied Mathematics) PDF

Best number systems books

Multidimensional Minimizing Splines: Theory and Applications

This e-book is of curiosity to mathematicians, geologists, engineers and, commonly, researchers and publish graduate scholars desirous about spline functionality idea, floor becoming difficulties or variational tools. From studies: The ebook is easily equipped, and the English is superb. i like to recommend the booklet to researchers in approximation concept, and to an individual attracted to bivariate facts becoming.

Expansions and Asymptotics for Statistics (Chapman & Hall/CRC Monographs on Statistics & Applied Probability)

Asymptotic tools supply vital instruments for approximating and analysing services that come up in likelihood and facts. additionally, the conclusions of asymptotic research usually complement the conclusions got by means of numerical tools. delivering a wide toolkit of analytical tools, Expansions and Asymptotics for facts exhibits how asymptotics, while coupled with numerical tools, turns into a strong strategy to gather a deeper figuring out of the concepts utilized in likelihood and facts.

Scientific Computing with Multicore and Accelerators (Chapman & Hall/CRC Computational Science)

The hybrid/heterogeneous nature of destiny microprocessors and massive high-performance computing platforms will bring about a reliance on significant different types of parts: multicore/manycore crucial processing devices and specific objective hardware/massively parallel accelerators. whereas those applied sciences have a number of advantages, in addition they pose huge functionality demanding situations for builders, together with scalability, software program tuning, and programming concerns.

Fixed Point of the Parabolic Renormalization Operator (SpringerBriefs in Mathematics)

This monograph grew out of the authors' efforts to supply a ordinary geometric description for the category of maps invariant less than parabolic renormalization and for the Inou-Shishikura mounted aspect itself in addition to to hold out a computer-assisted learn of the parabolic renormalization operator. It introduces a renormalization-invariant classification of analytic maps with a maximal area of analyticity and inflexible overlaying houses and provides a numerical scheme for computing parabolic renormalization of a germ, that is used to compute the Inou-Shishikura renormalization mounted element.

Extra info for Algorithmic Lie Theory for Solving Ordinary Differential Equations (Chapman & Hall/CRC Pure and Applied Mathematics)

Sample text

Download PDF sample

Rated 4.76 of 5 – based on 18 votes