Algorithmic Lie Theory for Solving Ordinary Differential by Fritz Schwarz

By Fritz Schwarz

although Sophus Lie's thought was once nearly the one systematic technique for fixing nonlinear usual differential equations (ODEs), it was once not often used for useful difficulties end result of the huge volume of calculations concerned. yet with the appearance of desktop algebra courses, it grew to become attainable to use Lie idea to concrete difficulties. Taking this process, Algorithmic Lie idea for fixing usual Differential Equations serves as a invaluable creation for fixing differential equations utilizing Lie's idea and comparable results.

After an introductory bankruptcy, the ebook offers the mathematical starting place of linear differential equations, overlaying Loewy's idea and Janet bases. the subsequent chapters current effects from the idea 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 booklet determine the symmetry periods to which quasilinear equations of order or 3 belong and remodel those equations to canonical shape. the ultimate chapters remedy the canonical equations and bring the final suggestions at any time when attainable in addition to offer concluding comments. The appendices comprise suggestions to chose workouts, worthwhile formulae, houses 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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