Algorithmic Lie Theory for Solving Ordinary Differential - download pdf or read online

By Fritz Schwarz

even though Sophus Lie's thought used to be almost the single systematic technique for fixing nonlinear usual differential equations (ODEs), it used to be hardly ever used for useful difficulties due to the tremendous quantity of calculations concerned. yet with the appearance of laptop algebra courses, it grew to become attainable to use Lie conception to concrete difficulties. Taking this strategy, Algorithmic Lie idea for fixing usual Differential Equations serves as a worthwhile creation for fixing differential equations utilizing Lie's conception and similar results.

After an introductory bankruptcy, the publication offers the mathematical starting place of linear differential equations, overlaying Loewy's idea and Janet bases. the next chapters current effects from the speculation of constant 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 publication determine the symmetry periods 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 overall strategies each time attainable in addition to supply concluding feedback. The appendices include recommendations to chose workouts, precious formulae, houses of beliefs of monomials, Loewy decompositions, symmetries for equations from Kamke's assortment, and a short 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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