The understanding of simulation semantics of a hybrid system is a challenge for computational engineers as it requires expertise in computer science, engineering, numerical methods, and mathematics at once. The testing methods for the execution of a simulation are being researched but not yet applied on the industrial level. Consequently, the semantics of the simulation becomes a critical artifact in the system development process. Embracing it from multiple design perspectives is going to create positive implications at the model, software, and hardware level. Hence, a set of self-testing algorithms for the simulation execution are proposed. Deploying them requires an inclusion of an additional testing dimension in the typical V diagram. Thus, a systematic methodology is conceptualized. A prototypical implementation takes advantage of the Simulink ® (1) simulation loop and (2) simulation state retrieval during the system model execution. These two artifacts allow to control and monitor the execution of a simulation. As a consequence, the semantics is systematically considered, its correctness is tested, and the numerical approximation is examined. A case study of a Cyber-Physical System illustrates conceptual and methodological aspects of the proposed algorithms.The ever growing pervasion of software-intensive systems into physical, technical, business, and social areas not only consistently increases the number of requirements on system functionality and features, but also puts forward ever stricter demands on system quality, reliability, safety, usability, etc. For example, Cyber-Physical Systems (CPS) [1], frequently characterized as smart systems include digital cyber technologies, software, and physical components and are intelligently interacting with other systems across information and physical interfaces. They are expressing an emerging behavior and so, create even more functionalities during the deployment ('live') to collaborate with each other more efficiently. CPS are sensing the external world and they immediately react on the state of the surrounding. Thus, in order to successfully develop such complex systems of systems and to additionally remain competitive, early and continuous consideration and assurance of system quality is becoming of vital importance.A challenging element of a CPS development process is its design phase. Here, selected features have to be accounted for and yet the entirety of the system has to be simulated in order to obtain knowledge and understanding about the dynamics and functionality of the system. This simulation, in turn, requires selected numerical integration methods (e.g., based on differential equations, difference equations, discrete events, discrete states, etc.[2]). Those methods include selected solvers and algorithms such as, control algorithms, optimization algorithms, integration and delay blocks, continuous-time elements, discrete-time elements, discreteevent elements, etc. to execute the system models. Thus, creating a CPS design implies a lot of algorit...