
Accession Number : AD0773658
Title : The Method of Lie Series for Differential Equations and Its Extensions.
Descriptive Note : Final technical rept.,
Corporate Author : INNSBRUCK UNIV (AUSTRIA) INST OF MATHEMATICS
Personal Author(s) : Wanner,G. ; Groebner,W. ; Fuchs,F. ; Hairer,E. ; Kirschner,O.
Report Date : SEP 1973
Pagination or Media Count : 162
Abstract : The work considers the initial value problem for an ordinary differential equation in a Banach space. The starting point of this research is Grobner's notation, the socalled Lie series. An explicit computation of the two normal subgroups whose product is the orthogonal group (and its transform) is given. A general method for the numerical integration of ordinary differential equations is studied. This method includes in special cases the multistep methods, RungeKutta methods (multistage), Taylor series (multi derivative) and their extensions. Finally, Euler's RungeKutta methods of type III(c) are considered and their Astability is proved. The implicit Euler's method is studied and is shown to be highly stable. An algorithm is implemented and numerical results are given. (Author)
Descriptors : *Differential equations, *Numerical integration, Boundary value problems, Banach space, Runge Kutta method, Iterations, Matrices(Mathematics), Austria
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE