Fritz Schwarz's Algorithmic Lie Theory for Solving Ordinary Differential PDF

By Fritz Schwarz

ISBN-10: 158488889X

ISBN-13: 9781584888895

although Sophus Lie's concept used to be almost the one systematic technique for fixing nonlinear usual differential equations (ODEs), it was once hardly ever used for useful difficulties as a result of the great quantity of calculations concerned. yet with the arrival of machine algebra courses, it grew to become attainable to use Lie conception to concrete difficulties. Taking this procedure, Algorithmic Lie concept for fixing usual Differential Equations serves as a invaluable creation for fixing differential equations utilizing Lie's conception and similar results.

After an introductory bankruptcy, the ebook offers the mathematical starting place of linear differential equations, protecting Loewy's concept and Janet bases. the next chapters current effects from the speculation of continuing teams of a 2-D manifold and talk about the shut relation among Lie's symmetry research and the equivalence challenge. The center chapters of the e-book determine the symmetry sessions to which quasilinear equations of order or 3 belong and remodel those equations to canonical shape. the ultimate chapters clear up the canonical equations and bring the overall options each time attainable in addition to offer concluding feedback. The appendices include ideas to chose routines, important formulae, houses of beliefs of monomials, Loewy decompositions, symmetries for equations from Kamke's assortment, and a quick description of the software program approach 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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