Konrad-Zuse-Zentrum für Informationstechnik Berlin

This reports presents new codes for the numerical solutiuon of highly nonlin-ear systems. They realize the most recent variants of aane invariant Newton Techniques due to Deuuhard. The standard method is implemented in the code NLEQ1, whereas the code NLEQ2 contains a rank reduction device additionally. The code NLEQ1S is the sparse version of NLEQ1, i.e. the arising linear systems are solved with sparse matrix techniques. Within the new implementations a common design of the software in view of user interface and internal modularization is realized. Numerical experiments for some rather challenging examples illustrate robustness and eeciency of algorithm and software.