Numerical methods for optimal control and especially software solutions remain an active research area in the mathematical and engineering community. The intention of this PhD thesis is to contribute to the development of reliable algorithms and software for optimal control and it is therefore focused on the popular direct single shooting method. An important computationally costly part of single shooting is the robust and efficient sensitivity analysis of the parameterized optimal control problems. Hence, to improve single shooting algorithms it is essential to investigate efficient numerical methods for sensitivity analysis. Another essentially open question is how to decide whether a direct single shooting solution sufficiently approximates the true solution of the underlying optimal control problem. Apart from the introduction (Chapter 1) and the summary (Chapter 6), this work contains four chapters which tackle the above mentioned issues. Chapter 2 is devoted to the theory of continuous sensitivity analysis which presents the following novel results: the discovery of composite adjoints to extend the classical adjoint sensitivity analysis to multi-point DAE embedded functionals of type f(z(t1),., z(tN), p) where z(t) is the solution of a differential-algebraic equations system; and the development of (higher-order) adjoint equations for non-smooth parametric semi-explicit differential-algebraic equations of index 1.Chapter 3 treats the theory of ODE and DAE constrained control problems, the analysis by means of the continuous necessary conditions of optimality and the verification of the numerical solution by a novel stopping criterion for single shooting. It provides a tailored literature overview and contains some novel contributions. It is discussed how to proper formulate ODE and DAE constrained optimal controls. In this context restrictions on the problem formulation are derived. For DAEs, these restrictions give rise to the classification of algebraic variables as volatile or non-volatile, a new concept introduced by the author. A conjecture is stated which characterizes the relations between the dual information of the NLP and the true solution with respect to the Minimum Principle of Pontryaginw. This conjecture is underpinned by a plausibility consideration and confirmed by numerical experiments. Furthermore, that conjecture is employed to construct a novel stopping criterion for adaptive shooting methods.Chapter 4 describes numerical methods, especially modified discrete adjoints of the linearly-implicit Euler's method. The efficiency-increasing modification of the discrete adjoints is essentially based on a simplification of the system's Jacobian. A convergence proof of the modified method is given. The modified discrete adjoint method is implemented in the (Nixe Is eXtrapolated Euler) solver. The NIXE solver is equipped with an efficient low-memory-consuming checkpointing scheme and with root-finding capabilities. A comparison of NIXE with the state-of-the-art continuous adjoint solver IDAS was given. Though IDAS is, as a multi-step method, typically faster for problems which are smooth on the whole time horizon, NIXE turns out to be more robust for the case studies under investigation. However, in the context of control vector parametrization, IDAS is outperformed by NIXE. In comparison with black box algorithmic differentiation, the tailored checkpointing of NIXE causes few computational overhead but reduces the memory requirements by several orders of magnitude.Chapter 5 introduces the AC-SAMMM platform, a computational framework for sensitivity analysis of Modelica models. Novel contributions include: the development of the Meta ESO class to parameterize models and an interface to the NIXE numerical solver; and the development of the algorithm to estimate the set of volatile algebraic variables which are related to restrictions in optimal control problem formulations.