Articles

In this paper, we will examine a rather complex case of the paradoxical nature of certain conclusions that may arise when studying the numerical convergence of a specific nonlinear recursive sequence, known in the literature as Muller’s sequence. To analyze the peculiar computational behavior of this sequence, it is necessary to employ a powerful mathematical framework in order to understand the nontrivial issues that can arise when the software implementation of this seemingly simple mathematical problem. These challenges often stem from the limitations of numerical methods and the inherent errors in computer arithmetic, which can affect the accuracy and stability of the results, particularly when dealing with iterative methods like Muller's sequence.

The paper presented the results of the research related to the analysis of the reliability of computer calculations. Relevant examples of incorrect program operation were demonstrated: both quite simple and much less obvious, such as S. Rump's example. In addition to mathematical explanations, authors focused on purely software capabilities for controlling the accuracy of complex calculations. For this purpose, examples of effective use of the functionality of the decimal and fraction modules in Python 3.x were given.

Due to its geographical location, Iran has numerous capacities in renewable energy, and this issue has made the need to develop renewable energy on the authorities’ agenda. This underscores the need to provide an optimal model for developing renewable energy. Therefore, in this study, the main purpose was to provide an optimal renewable energy model. In line with this goal, by choosing the cost function as the objective function and considering the potential constraints of renewable energy (resource constraints), the amount of electricity consumption in each of the 16 electricity regions (demand constraint) and the limitation of renewable energy production coefficient (Technical constraints), the optimal model of renewable energy use was designed and solved using a solid programming model in LINGO software. The optimal model results show 15.19% small hydropower, 24.30% wind energy, 5.52% biomass energy, 6.13% is geothermal energy, 4.79% is tidal energy, and 44.07% solar energy. The optimum portfolio of renewable energy is estimated in this paper using the robust optimization approach. The results showed which renewable technology has the greater potential to take more share of the energy portfolio. The results of this investigation help policymakers to choose the most suitable renewable technologies to support.