This paper presents a method for predicting the energy yield of a photovoltaic (PV) system based on the ARIMA algorithm. We analyze two key time series: the specific yield and the total yield of the PV system. Two ARIMA models are developed for each time series: one selected by the authors and one determined by SPSS. Model performance is evaluated through fit statistics, providing a comprehensive assessment of model accuracy. The residuals’ ACF and PACF are examined to ensure model adequacy, and confidence intervals are calculated for residuals to validate the models. A monthly forecast is then generated for both time series, complete with confidence intervals, to demonstrate the models’ predictive capabilities. The results highlight the effectiveness of ARIMA in forecasting PV energy yields, offering valuable insights for optimizing PV system performance and planning. This study contributes to the field of renewable energy forecasting by demonstrating the applicability of ARIMA models in predicting the monthly performance of photovoltaic systems.

Mathematical modeling of the heat transfer during the pyrolysis process used for the treatment of the End-of-Lifetires (EOLT) is presented in this paper. The pyrolysis process is 3D and non-stationary and because of this it is very complicated for modeling and studying. To simplify the modeling here a hierarchy of 2D models for the temperature which describe the non-stationary heat transfer in such a pyrolysis station is created. An algorithm for solving the model equations, based on MATLAB software is developed. The results for the temperature for some characteristic periods of operation of pyrolysis station are presented and commented in the paper. The results from this modeling can be used in the real pyrolysis station for more precise displacement of measurement devices and for designing of automated management of the process.

Indoor air quality plays a crucial role in human health and well-being, with relative humidity (RH) being a key factor influencing respiratory health, indoor comfort, and the interior lifespan of buildings. Poor RH control can exacerbate indoor air pollution, leading to adverse health effects and increased risks of microbial growth. This study created a predictive approach to indoor RH management by developing an intelligent electronic system that proactively regulates a humidifier and dehumidifier to maintain optimal humidity levels. The system integrates a forecasting algorithm based on the ARIMA model, enabling short-term RH predictions and dynamic adjustments before extreme conditions occur. The ARIMA model was selected for its robustness in time-series forecasting, ensuring precise predictions and improved indoor climate regulation. The results demonstrate that this predictive control strategy significantly reduces fluctuations in RH, preventing the effects of indoor air pollution associated with humidity extremes while enhancing energy efficiency. Additionally, the iterative validation process confirms the model’s reliability and adaptability to changing environmental conditions. This study suggests the importance of predictive RH control in mitigating the threat of poor indoor air quality, improving indoor comfort, and promoting energy-efficient and sustainable living environments.

FEM for a linear and nonlinear elliptic interface problems with discontinuous coefficients is presented. The standard basis functions are modified near the interface in such a way that they satisfy the jump conditions on the interface. Convergence of the method is discussed and numerical experiments, confirming second order of accuracy are shown.

In this paper we study the problem of a load, traveling along elastic structures, such as strings, beams or plates. The case of semi‐active viscous dampers is also considered. The numerical method, based on the Immersed Interface Finite Element Method is developed. The presence of Dirac‐delta function terms in the mathematical model leads to using of a special basis functions near the interfaces. Many numerical experiments are presented for different practical cases.