Accession Number : AD0773658

Title :   The Method of Lie Series for Differential Equations and Its Extensions.

Descriptive Note : Final technical rept.,


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 so-called 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 multi-step methods, Runge-Kutta methods (multistage), Taylor series (multi derivative) and their extensions. Finally, Euler's Runge-Kutta methods of type III(c) are considered and their A-stability 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