Abstract
In this chapter we consider the solution of the model equations of water supply networks and continuous optimal control tasks. We begin with the description of our simulation tool in Sect. 2.1, in particular the numerical treatment of the water hammer equations. This includes the description of the implemented discretization scheme together with a stability and convergence analysis. As we will see, the applied scheme perfectly matches with the properties of the water hammer equations and thus builds a useful foundation for the solution of the entire model equations as well as optimal control tasks.
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