Extrapolation Integrators for Quasilinear Implicit ODEs

Abstract

This paper Heals with quasilinear implicit ODEs of the form

$$ {\text{B}}\left( {\text{y}} \right){\text{y' = f}}\left( {\text{y}} \right) $$

((0.1))

.The main emphasis of the paper will be on problems, where B is nonsingu-lar (index = 0). Extensions to problems with index = 1, where B is singular, are also included. In large scale scientific computing, problems of the type (0.1) may arise e.g. in chemical reaction kinetics, when thermodynamic equations are added, or in method of lines treatment for time-dependent PDEs with moving spatial grids (compare Miller [8,9], Hyman [6]).