Abstract The recently developed new algorithm for computing consistent initial values and Taylor coefficients DAEs using projector-based constrained optimization opens possibilities to apply series integration methods. In this paper, we show how corresponding projected explicit implicit methods can be adapted of arbitrary index. Owing our formulation as a problem by the derivative array, no des...

Simulating the dynamics of many-body quantum systems is believed to be one first fields that computers can show a advantage over classical computers. Noisy intermediate-scale (NISQ) algorithms aim at effectively using currently available hardware. For simulation, various types NISQ have been proposed with individual advantages as well challenges. In this work, we propose new algorithm, truncate...

An infinite-dimensional bilinear optimal control problem with infinite-time horizon is considered. The associated value function can be expanded in a Taylor series around the equilibrium, the Taylor series involving multilinear forms which are uniquely characterized by generalized Lyapunov equations. A numerical method for solving these equations is proposed. It is based on a generalization of ...