Managing the drift-off in numerical index-2 differential algebraic equations by projected defect corrections

Abstract

When integrating index-2 differential-algebraic equations, the given constraint may be failed to be met due to the integration method itself and also due to numerical defects in the realization. This so-called drift-off gives rise to bad instabilities. In 1991 Ascher and Petzold proposed to manage the drift-off caused by symmetric implicit Runge-Kutta methods in Hessenberg systems by means of backprojections onto the constraint. In the present paper, this nice idea is generalized and analyzed in some detail for general index-2 differential-algebraic equations and, in particular, for quasilinear equations a(x,t)x' + g(x,t) = 0, as they arise in applications. Now the constraint under consideration is only implicitly given and the backprojection turns out to be rather a projected defect correction.