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 was once almost the one systematic approach for fixing nonlinear traditional differential equations (ODEs), it used to be infrequently used for useful difficulties due to the substantial quantity of calculations concerned. yet with the appearance of desktop algebra courses, it turned attainable to use Lie conception to concrete difficulties. Taking this procedure, Algorithmic Lie conception for fixing traditional Differential Equations serves as a worthwhile creation for fixing differential equations utilizing Lie's thought and comparable results.

After an introductory bankruptcy, the ebook presents the mathematical beginning of linear differential equations, protecting 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 center chapters of the ebook 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 convey the overall options at any time when attainable in addition to supply concluding feedback. The appendices comprise options 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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