Time-dependent linear DAEs with discontinuous inputs Original Research Article

Existence and uniqueness results are proved for initial-value problems associated with linear, time-varying, differential-algebraic equations. The right-hand sides are chosen in a space of distributions allowing for solutions exhibiting discontinuities as well as impulses. This approach also provides a satisfactory answer to the problem of inconsistent initial conditions, of crucial importance for physical applications. Furthermore, our theoretical results yield an efficient numerical procedure for the calculation of the jump and impulse of a solution at a point of discontinuity. Numerical examples are given.