Time-dependent linear DAEs with discontinuous inputs (Q2564943)

The paper proves existence and uniqueness results for linear time varying differential algebraic equations (DAEs) with discontinuities in the right hand side, i.e. for problems of the type, \(A(t)x'(t) + B(t)x(t) = f(t)\), where \(f(t)\) exhibits jumps. It turns out that the question of consistency of initial conditions can conveniently be represented in this way. Furthermore the theoretical results lead to a numerical procedure for calculation of the jump and impulse of the solution at the point of a discontinuity. Finally some numerical examples for illustrating the algorithm are presented.