Accession Number : AD0716343

Title :   Development of New Methods for the Solution of Nonlinear Differential Equations by the Method of Lie Series and Extension to New Fields.

Descriptive Note : Final technical rept. Oct 69-Sep 70,

Corporate Author : INNSBRUCK UNIV (AUSTRIA) DEPT OF MATHEMATICS

Personal Author(s) : Groebner,W. ; Kuhnert,K. ; Reitberger,H. ; Wanner,G.

Report Date : OCT 1970

Pagination or Media Count : 120

Abstract : 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)

Descriptors :   (*NONLINEAR DIFFERENTIAL EQUATIONS, NUMERICAL METHODS AND PROCEDURES), OPERATORS(MATHEMATICS), GROUPS(MATHEMATICS), MATRICES(MATHEMATICS), PERTURBATION THEORY, INTEGRAL EQUATIONS, ITERATIONS, NUMERICAL INTEGRATION, TRANSFORMATIONS(MATHEMATICS), SERIES(MATHEMATICS), ITERATIONS, AUSTRIA

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE