Fritz Schwarz's 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 nearly the single systematic technique for fixing nonlinear traditional differential equations (ODEs), it used to be not often used for sensible difficulties as a result huge volume of calculations concerned. yet with the arrival of computing device algebra courses, it turned attainable to use Lie concept to concrete difficulties. Taking this technique, Algorithmic Lie concept for fixing usual Differential Equations serves as a worthwhile advent for fixing differential equations utilizing Lie's idea and comparable results.

After an introductory bankruptcy, the publication presents the mathematical beginning 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 speak about the shut relation among Lie's symmetry research and the equivalence challenge. The middle chapters of the publication determine the symmetry periods to which quasilinear equations of order or 3 belong and rework those equations to canonical shape. the ultimate chapters clear up the canonical equations and bring the overall strategies every time attainable in addition to supply concluding feedback. The appendices comprise options to chose workouts, invaluable formulae, houses of beliefs of monomials, Loewy decompositions, symmetries for equations from Kamke's assortment, and a quick description of the software program method 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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