Development of New Methods for the Solution of Nonlinear Differential Equations by the Method of Lie Series and Extension to New Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Development of New Methods for the Solution of Nonlinear Differential Equations by the Method of Lie Series and Extension to New Fields write by W. Groebner. This book was released on 1970. Development of New Methods for the Solution of Nonlinear Differential Equations by the Method of Lie Series and Extension to New Fields available in PDF, EPUB and Kindle. Chapter 1 of the report gives an application of the well experienced method of Lie series to the theory of Lie groups. First, find a representation of these functions by Lie series. The operators are commutative and contain a matrix of functions w sub ik(x;y) the infinitesimal transformations and the connected Lie algebra, or Lie ring more generally, of a given Lie group are derived. Linear infinitesimal operators are developed in detail the construction of the invariants belonging to these groups with the help of Lie series is demonstrated. A new method for finding subgroups is shown. A new derivation of the Campbell-Baker-Hausdorff-Formula and improvement to the Cayley Theorem is given. Chapter 2 clears the connection between the perturbation formulas of Groebner (1960) and Alexseev (1961) for the solution of ordinary differential equations. These formulas are generalized and iteration methods are given, which include the Methods of Picard, Groebner-Knapp, Poincare, Chen, as special cases. Chapter 3 generalizes an iterated integral equation of Chen and indicates an iteration method based on this generalization. A compound form combining the generalization with Groebner's perturbation formula is furnished. (Author).
Development of New Methods for the Solution of Nonlinear Differential Equations by the Method of Lie Series and Extension to New Fields
Development of New Methods for the Solution of Nonlinear Differential Equations by the Method of Lie Series and Extension to New Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Development of New Methods for the Solution of Nonlinear Differential Equations by the Method of Lie Series and Extension to New Fields write by Wolfgang Gröbner. This book was released on 1970. Development of New Methods for the Solution of Nonlinear Differential Equations by the Method of Lie Series and Extension to New Fields available in PDF, EPUB and Kindle.
Bibliography of Scientific and Industrial Reports
Bibliography of Scientific and Industrial Reports - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Bibliography of Scientific and Industrial Reports write by . This book was released on 1970. Bibliography of Scientific and Industrial Reports available in PDF, EPUB and Kindle.
U.S. Government Research & Development Reports
U.S. Government Research & Development Reports - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook U.S. Government Research & Development Reports write by . This book was released on 1971. U.S. Government Research & Development Reports available in PDF, EPUB and Kindle.
Development of New Methods for the Solution of Differential Equations by the Method of Lie Series
Development of New Methods for the Solution of Differential Equations by the Method of Lie Series - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Development of New Methods for the Solution of Differential Equations by the Method of Lie Series write by W. Groebner. This book was released on 1969. Development of New Methods for the Solution of Differential Equations by the Method of Lie Series available in PDF, EPUB and Kindle. The report summarizes the recent work in the application of the LIE-series method to the solution of ordinary and partial differential equations. The power series method which is a special case of the Lie series method of chapter III is described in chapter II. Chapter III deals with the numerical evaluation of the Lie series perturbation formula. In chapter IV we prove Grobner's integral equation which leads to short proofs of the formulas of chapter III and to various generalizations of the method. A survey of these is presented at the end of this summary. Chapter V generalizes the concept of Runge-Kutta to methods with multiple nodes, which is possible with the use of the Lie differential operator D. Chapter VI deals with the step-size control and chapter VII shows the application of generalized Lie series to the calculation of switch-on transients occurring in the telegraphic equation.
