ON THE REGULARIZATION OF INDEX 2 DIFFERENTIAL-ALGEBRAIC EQUATIONS

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)). © 1990.