Accession Number : AD0696495

Title :   DEVELOPMENT OF NEW METHODS FOR THE SOLUTION OF DIFFERENTIAL EQUATIONS BY THE METHOD OF LIE SERIES

Descriptive Note : Final technical rept. Jun 1968-Jul 1969

Corporate Author : INNSBRUCK UNIV (AUSTRIA) INST OF MATHEMATICS

Personal Author(s) : Groebner, W ; Kestlunger, K H ; Reitberger, H ; Saely, R ; Wanner, G

PDF Url : AD0696495

Report Date : Jul 1969

Pagination or Media Count : 160

Abstract : 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.

Descriptors :   *DIFFERENTIAL EQUATIONS, *NUMERICAL ANALYSIS, *NUMERICAL INTEGRATION, AUSTRIA, BOUNDARY VALUE PROBLEMS, INTEGRAL EQUATIONS, ITERATIONS, PARTIAL DIFFERENTIAL EQUATIONS, PERTURBATION THEORY, POWER SERIES, RECURSIVE FUNCTIONS, SERIES(MATHEMATICS), TELEGRAPH SIGNALS, TRANSIENTS

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE