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

By Fritz Schwarz

ISBN-10: 158488889X

ISBN-13: 9781584888895

even though Sophus Lie's idea used to be nearly the one systematic approach for fixing nonlinear usual differential equations (ODEs), it used to be hardly ever used for sensible difficulties as a result sizeable volume of calculations concerned. yet with the appearance of machine algebra courses, it grew to become attainable to use Lie thought to concrete difficulties. Taking this method, Algorithmic Lie thought for fixing usual Differential Equations serves as a worthwhile advent for fixing differential equations utilizing Lie's concept and comparable results.

After an introductory bankruptcy, the publication presents the mathematical origin of linear differential equations, protecting Loewy's concept and Janet bases. the subsequent 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 establish the symmetry periods to which quasilinear equations of order or 3 belong and rework those equations to canonical shape. the ultimate chapters resolve the canonical equations and bring the overall options each time attainable in addition to offer concluding feedback. The appendices include suggestions to chose routines, invaluable formulae, homes of beliefs of monomials, Loewy decompositions, symmetries for equations from Kamke's assortment, and a short 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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