On the regularization of index 2 differential-algebraic equations

Abstract

Boundary value problems for linear differential-algebraic equations (DAEs) with time-varying coefficients A( t) x′( t) + B( t) x( t) = q( t) tractable with index 2 are considered. These DAEs contain differentiation problems and lead, therefore, to essentially ill-posed problems. We show that a parametrization proposed by März is a regularization in the sense of Tikhonov. Convergence rates for noisy data are derived. Moreover, for the so-called pencil regularization, analogous results are derived in the case of a time-independent nullspace N( A( t)).