We present our numerical simulation approach for the End-to-End (E2E) model applied to various astronomical spectrographs, such as SOXS (ESO-NTT), CUBES (ESO-VLT), and ANDES (ESO-ELT), covering multiple wavelength regions. The E2E model aim at simulating the expected astronomical observations starting from the radiation of the scientific sources (or calibration sources) up to the raw-frame data produced by the detectors. The comprehensive description includes E2E architecture, computational models, and tools for rendering the simulated frames. Collaboration with Data Reduction Software (DRS) teams is discussed, along with efforts to meet instrument requirements. The contribution to the cross-correlation algorithm for the Active Flexure Compensation (AFC) system of CUBES is detailed.
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