Accession Number : AD0746276

Title :   The Solution of Differential Equations by the Method of Lie Series and Its Generalizations.

Descriptive Note : Final technical rept. 1 Apr 71-31 Mar 72,

Corporate Author : INNSBRUCK UNIV (AUSTRIA) INST OF MATHEMATICS

Personal Author(s) : Grobner,W. ; Fuchs,F. ; Hairer,E. ; Kuhnert,K. ; Kastlunger,K.

Report Date : APR 1972

Pagination or Media Count : 126

Abstract : As a part of the Lie Series, there is an operator D which operates on differentiable functions. A computer program to perform the differentiations automatically was prepared previously. A generalized Runge-Kutta (RK) method for handling multiple nodes was developed. They can be applied to stiff differential equations. An integration process was developed which includes as special cases such techniques as Power Series, multi-step methods, RK, RK with multiple nodes, pseudo RK etc. The Grobner-Alekseev formula, previously generalized for integro-differential equations has now been generalized for arbitrary operator differential equations. The iterative solution of the Grobner formula is shown to converge under certain conditions and estimates are given for the domain of convergence and the error. (Author)

Descriptors :   (*DIFFERENTIAL EQUATIONS, NUMERICAL INTEGRATION), BOUNDARY VALUE PROBLEMS, INTEGRAL EQUATIONS, SERIES(MATHEMATICS), ITERATIONS, GROUPS(MATHEMATICS), MATRICES(MATHEMATICS), CONVERGENCE, AUSTRIA

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE