Read e-book online Algorithmic Lie Theory for Solving Ordinary Differential PDF

By Fritz Schwarz

ISBN-10: 158488889X

ISBN-13: 9781584888895

although Sophus Lie's idea used to be almost the single systematic approach for fixing nonlinear usual differential equations (ODEs), it used to be infrequently used for functional difficulties as a result of the huge quantity of calculations concerned. yet with the appearance of desktop algebra courses, it turned attainable to use Lie thought to concrete difficulties. Taking this strategy, Algorithmic Lie thought for fixing traditional Differential Equations serves as a invaluable advent for fixing differential equations utilizing Lie's conception and comparable results.

After an introductory bankruptcy, the ebook offers the mathematical origin of linear differential equations, protecting Loewy's idea and Janet bases. the next chapters current effects from the speculation of constant teams of a 2-D manifold and talk about the shut relation among Lie's symmetry research and the equivalence challenge. The middle chapters of the e-book 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 bring the overall suggestions every time attainable in addition to supply concluding comments. The appendices comprise ideas to chose routines, beneficial formulae, homes of beliefs of monomials, Loewy decompositions, symmetries for equations from Kamke's assortment, and a quick description of the software program process ALLTYPES for fixing concrete algebraic problems.

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Algorithmic Lie Theory for Solving Ordinary Differential Equations (Chapman & Hall/CRC Pure and Applied Mathematics) by Fritz Schwarz


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