Download e-book for iPad: Algorithmic Lie Theory for Solving Ordinary Differential by Fritz Schwarz

By Fritz Schwarz

although Sophus Lie's conception used to be almost the single systematic technique for fixing nonlinear usual differential equations (ODEs), it was once infrequently used for functional difficulties as a result of the tremendous quantity of calculations concerned. yet with the arrival of computing device algebra courses, it grew to become attainable to use Lie concept to concrete difficulties. Taking this method, Algorithmic Lie concept for fixing traditional Differential Equations serves as a precious creation for fixing differential equations utilizing Lie's idea and similar results.

After an introductory bankruptcy, the publication presents the mathematical starting place 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 e-book establish the symmetry sessions to which quasilinear equations of order or 3 belong and rework those equations to canonical shape. the ultimate chapters remedy the canonical equations and bring the final ideas at any time when attainable in addition to offer concluding feedback. The appendices include suggestions to chose routines, worthwhile formulae, houses of beliefs of monomials, Loewy decompositions, symmetries for equations from Kamke's assortment, and a quick description of the software program procedure 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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