The electron flow through quantum waveguides is modeled by the time-dependent Schrödinger equation with absorbing boundary conditions, which are realized by a negative imaginary potential. The Schrödinger equation is discretized by a time-splitting spectral method, and the quantum waveguides...

The index of differential-algebraic equations is one measure for the numerical problems in electric circuit simulation. The index depends on the mathematical model in different ways: setup of equations, classical or charge-oriented formulation and modelling of basic elements and semiconductor...

In electrical circuit simulation, a refined network approach is used to describe secondary and parasitic effects. This ansatz yields initial-boundary value problems of mixed partial-differential and differential-algebraic equations, so-called PDAE systems. One requirement for method-of-lines...