Mathematical modeling of the energy consumption problem; [Энергияны тұтыну мәселелерiн математикалық модельдеу]; [Математическое моделирование проблемы энергопотребления]

The importance of energy-saving and correct design is obvious for energy efficiency. Correct design means that before construction considerable things, such as orientation or isolation decisions, need to be made. This study gives a mathematical model of the nonstationary energy consumption calculation problems. The model is well-posedness in Holder spaces of the mixed one-dimensional parabolic problem with Robin boundary conditions. In this study, an effective numerical method is also developed for energy consumption calculation which is related to this mathematical model. The three case problems are taken to test this numerical method. The dynamic model results have been compared with the previous finite-difference or steady-state solutions. The study also aims to develop a mathematical model in which the result can be found at any time. © The Author(s) 2022.