The Method of Lie Series for Differential Equations and Its Extensions.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1973
- Accession Number
- AD0773658
Entities
People
- E. Hairer
- F. Fuchs
- G. Wanner
- O. Kirschner
- W. Groebner
Organizations
- University of Innsbruck