AI-Enhanced Performance Evaluation of Python, MATLAB, and Scilab for Solving Nonlinear Systems of Equations: A Comparative Study Using the Broyden Method

Azure, Isaac; Wiredu, Japheth Kodua; Musah, Anas; Akolgo, Eric

doi:10.4236/ajcm.2023.134036

Cited by 4 publications

(1 citation statement)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This is an open-source numerical algebra system that has been successfully used to solve most mathematical problems related to matrices, numerical methods, etc. [59]. It ensures that there are no additional oscillations and provides a straight horizontal line if two points have the same ordinate.…”

Section: Rain Eventmentioning

confidence: 99%

Improving the Efficiency and Environmental Friendliness of Urban Stormwater Management by Enhancing the Water Filtration Model in Rain Gardens

Kravchenko,

Trach,

Trach

et al. 2024

Water

View full text Add to dashboard Cite

Rain gardens are used to solve urban problems related to the negative impact of stormwater. (1) Scientific contributions from different countries provide general guidelines for the design and operation of rain gardens in different geographical areas. Given the small spatial scale of rain gardens, the use of existing infiltration models often leads to design errors. (2) The purpose of this paper is to develop a hydrological model by introducing a system of equations that extends the ability to calculate the rate, flow rate and time of saturation of layers with moisture and rainwater leakage from the rain garden system. (3) The results obtained allow us to describe the dynamic processes of passage and saturation of layers of the rain garden at a certain point in time, which extends the ability to calculate the flow rate. It was established that the smaller the area of the rain garden compared to the area of the catchment basin, the faster it reaches its full saturation. Increasing the thickness of the rain garden layers allows for an increase in the efficiency of water retention at a lower value of the area ratio. (4) The practical significance of the results obtained is especially important for the correct description of hydrodynamics in the system and determining the optimal conditions for the effective functioning and management of the rain garden structure for any climatic region.

show abstract

Section: Rain Eventmentioning

confidence: 99%

Improving the Efficiency and Environmental Friendliness of Urban Stormwater Management by Enhancing the Water Filtration Model in Rain Gardens

Kravchenko,

Trach,

Trach

et al. 2024

Water

View full text Add to dashboard Cite

show abstract

Improving Urban Stormwater Management Using the Hydrological Model of Water Infiltration by Rain Gardens Considering the Water Column

Kravchenko,

Wrzesiński,

Pawluk

et al. 2024

Water

View full text Add to dashboard Cite

Implementing rain garden (RG) designs is widespread worldwide to reduce peak flow rates, promote stormwater infiltration, and treat pollutants. However, inadequate RG design degrades its hydrological behaviour, requiring the development and validation of an appropriate hydrological model for the design and analysis of structures. This study aimed to improve a hydrological infiltration model based on Darcy’s law by taking into account the height of the water column (HWC) at the surface of the RG and the filtration coefficients of soil materials. The model was tested by simulating the hydrological characteristics of a rain garden based on a single rain event of critical intensity (36 mm/h). Using the validated model, design curves were obtained that predict the performance of the RG as a function of the main design parameters of the structure: water column height, ratio of catchment area to structure area, layer thickness, and soil filtration coefficient. The hydrological efficiency of the RG was evaluated in terms of the time of complete saturation, filling of the structure with water, and determining the change in HWC caused by changes in the parameters. The filtration coefficient and thickness of the upper and intermediate infiltration layers of the RG are the main parameters that affect the depth of saturation of the layers of the structure and the HWC on the surface. The model is not very sensitive to the model parameters related to the lower gravel layer. If the top layer’s thickness increases by 10 cm, it takes longer to fill the structure with water, and the HWC on the surface reaches 0.341 m. The rain garden’s performance improves when the filtration coefficient of the top layer is 7.0 cm/h. Complete saturation and filling of the structure with rainwater do not occur within 7200 s, and the water column reaches a height of 0.342 m at this filtration coefficient. However, the rain garden’s effectiveness decreases if the filtration coefficient of the upper and intermediate layers exceeds 15 cm/h and 25 cm/h, respectively, or if the catchment area to RG area ratio decreases to values below 15. The modelling results confirm that considering the HWC in RG hydrological models is essential for designing structures to minimise the risk of overflow during intense rainfall events.

show abstract

Efficiency Analysis and Optimization Techniques for Base Conversion Algorithms in Computational Systems

Kodua Wiredu,

Atiyire,

Seidu Abuba

et al. 2024

International Journal of Innovative Science and Research Techno

View full text Add to dashboard Cite

The performance of base conversion methods varies greatly across several techniques, and this is important for computer-based systems. This research paper therefore examines the efficiency of three base conversion methods namely; Successive Multiplication Method, Positional Notation Method, and Horner’s Method. Their execution times are evaluated for binary, octal, decimal, and hexadecimal bases with input sizes that range from 1000 to 10,000 digits. Empirical results show that on average Horner’s Method outperforms other methods by having about 40% better execution times and up to 30% more uniformity than Positional Notation Method based upon repeated application of decimal points. Specifically speaking, for hexadecimal conversions, it took on average 0.009 seconds for Horner’s method as against 0.460 seconds for Positional Notation and another 0.009 seconds Successive Multiplication method. These observations indicate that Horner’s method is the most efficient in terms of time taken during a base conversion process as well as its consistency when compared to other techniques used in performing the same task throughout different bases such as decimal point addition repeatedly considered in positional notation numeral system. Notably, Horner’s Method completed a hexadecimal conversion at an average rate of one every nine milliseconds on the other hand the Positional Notation Approach finished one conversion per second while the Successive Multiplication Technique performed at best zero conversions within a given unit of time. It accomplishes these tasks much faster than previous approaches because it does not require multiplication steps or many intermediate calculations before obtaining answers like in Problem I; instead, only a few additions per digit are required which can be done more quickly using modern hardware such as programmable logic arrays (PLAs) according to writer P1 - R3 or even printed circuit boards (PCBs).

show abstract

AI-Enhanced Performance Evaluation of Python, MATLAB, and Scilab for Solving Nonlinear Systems of Equations: A Comparative Study Using the Broyden Method

Cited by 4 publications

References 16 publications

Improving the Efficiency and Environmental Friendliness of Urban Stormwater Management by Enhancing the Water Filtration Model in Rain Gardens

Improving the Efficiency and Environmental Friendliness of Urban Stormwater Management by Enhancing the Water Filtration Model in Rain Gardens

Improving Urban Stormwater Management Using the Hydrological Model of Water Infiltration by Rain Gardens Considering the Water Column

Efficiency Analysis and Optimization Techniques for Base Conversion Algorithms in Computational Systems

Contact Info

Product

Resources

About