Lie-Theoretic Ode Numerical Analysis, Mechanics and Differential Systems - ISBN:0915692457

Lie-Theoretic Ode Numerical Analysis, Mechanics and Differential Systems

Date: 14 April 2011, 13:58

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For the past four years, my work has focused on two areas: The Lie and Deformation Theory of standard ODE Numerical Analysis and the Differential-Geometric and Lie-Cartan Theoretic aspects of the Generalized Function Algebra Theory of Colombeau, Oberguggenberger and Rosinger. In this Volume I concentrate on the first topic: I hope to get to the second topic in a more systematic way in Vol. 30.
My broad aim on the 'Numerical Analysis of DE's Side' is to develop it as an Extension (or a Deformation!) of the 'Geometric Theory of Differential Systems', as developed by Lie, Goursat, Cartan, Vessiot, Spencer, ....The rest of the Volume deals with more specific parts of what I ultimately hope will be a broad 'Theory of Mechanics Differential Systems, and Their Discrete Approximations'. I concentrate here on ODE's and certain PDE Systems whose 'General Solution' can be found by solving ODE's. On the Applied side, I hope to provide new geometric methodology for thinking about ODE Numerical Analysis, particularly for ODE's which 'live' on general manifolds and those which naturally involve Lie Groups and certain Infinite Lie-Spencer Pseudogroups, such as the Symplectic Pseudogroup which underlies Mechanics. AS in previous Volumes, 1 begin with Polemic, Notes on Lectures, and Introductions.

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