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 68-Jul 69,

Corporate Author : INNSBRUCK UNIV (AUSTRIA) DEPT OF MATHEMATICS

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

Report Date : JUL 1969

Pagination or Media Count : 164

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

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE