
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 7131 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 RungeKutta (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, multistep methods, RK, RK with multiple nodes, pseudo RK etc. The GrobnerAlekseev formula, previously generalized for integrodifferential 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