By Fritz Schwarz

even though Sophus Lie's concept was once almost the one systematic strategy for fixing nonlinear traditional differential equations (ODEs), it was once hardly used for functional difficulties a result of vast quantity of calculations concerned. yet with the appearance of computing device algebra courses, it turned attainable to use Lie thought to concrete difficulties. Taking this technique, Algorithmic Lie concept for fixing traditional Differential Equations serves as a worthy creation for fixing differential equations utilizing Lie's thought and comparable results.

After an introductory bankruptcy, the publication offers the mathematical beginning of linear differential equations, masking Loewy's conception and Janet bases. the next 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 middle chapters of the publication establish the symmetry sessions to which quasilinear equations of order or 3 belong and remodel those equations to canonical shape. the ultimate chapters resolve the canonical equations and convey the overall recommendations at any time when attainable in addition to supply concluding comments. The appendices include recommendations to chose workouts, helpful 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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