Orthogonal Boubaker-Turki polynomials algorithm for problems arising in engineering

Alabdali, Osama; Shihab, Suha; Rasheed, Mohammed; Rashid, Taha

doi:10.1063/5.0066860

Cited by 16 publications

(7 citation statements)

References 17 publications

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“…The highest rates were recorded in the winter season in site (1) with a limit of (131 µg/L), and the lowest rates were recorded in the spring season in site ( 5) at (18 µg/L). Despite the presence of the As element in varying amounts in the sediments of all four locations and seasons, the results showed that the concentrations of the As element were higher than the minimum concentration of As set by the World Health Organization and estimated that the concentrations of As were higher than the minimum concentration of As set by the European Union (WHO 2022) (7 µg/L) [36]. As Arsenic is present with oil derivatives, the increase in As concentration may be caused by the numerous water pumps that farmers use to raise water from the river to nearby lands and the resulting smoke and waste, or it may be caused by the frequent use of fertilizers by farmers that reach the river through the flow of large amounts of water to it as a result of the sharp decline of agricultural Arsenic is present at high concentrations in Iraqi phosphate fertilizers.…”

Section: Discussionmentioning

confidence: 76%

“…As a result of Al-Iraqi's rapid reaction rate with an alkaline media, the adsorption of heavy metals is increased. These findings suggest that the Cn levels were over the 70 µg/L (WHO 2022) limit set by the World Health Organization [36]. This is a warning sign indicating a major threat to living things' health.…”

Section: Discussionmentioning

confidence: 78%

“…Pearson Correlation Coefficient (R) [30][31][32], and P Value from Pearson (R) [33][34][35][36] of all the variables under test.…”

Section: Discussionmentioning

confidence: 99%

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A study of Physicochemical Parameters, Heavy Metals and Algae in the Euphrates River, Iraq

Hussein,

Al-Darraji,

Rasheed

2023

IOP Conf. Ser.: Earth Environ. Sci.

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For many individuals, heavy metal persistence and toxicity are severe problems. Most of these heavy metals collect in wastewater from effluents discharged by various industries. The efficient re-use of these particles as catalysts is another new development in research that complements the success of hazardous metal particle removal. Five locations along the Euphrates River in western Iraq’s Anbar Governorate were the subject of the research (Husaibah Al-Sharqiah, Al-Karābilah, Barwana, Al-Garma, Al-Forat sub district) and for four seasons (Summer, Autumn, Winter, and Spring) from November 2021 to November 2022 in order to examine how the physical and chemical characteristics of the water in the Euphrates River vary over space and time in these areas. Based on these locations of garbage, contaminants, and heavy metal components that may flow into the river without environmental management, sampling locations on the Euphrates River were chosen. In order to better understand the distribution of heavy metals (HMs: Arsenic (As), Antimony (Sb), Selenium (Se), Molybdenum (Mo), Cyanide (CN-), and Chromium (Cr) in river sediments, five locations in western Iraq were chosen for the research. The PH, electrical conductivity (EC), algaes, and sediments (Nitrate (NO3), sulfate (SO4), and HMs content) were all measured in the river’s edge water. A qualitative research was also carried out at various times of year and locations. 104 different kinds of algae were found, and some of them dominated all the research locations. In each station near the beginning of the estuary, the quantitative research revealed a rise in the number of algae species indicative of pollution, confirming that these sites are impacted by the pollutants from untreated sewage discharged into the Euphrates River in those locations. The average concentrations of HMs and compounds in the sediments were as follows: SO4> NO3>Mo>Cn>Cr>Sb>Se>As. According to the investigation, the HMs polluted cities in the following ways: Sediment concentrations are greater in Husaibah Al-Sharqiah, Al-Karbilah, Barwana, Al-Garma, and Al-Forat subdistrict cities.

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Section: Discussionmentioning

confidence: 76%

Section: Discussionmentioning

confidence: 78%

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A study of Physicochemical Parameters, Heavy Metals and Algae in the Euphrates River, Iraq

Hussein,

Al-Darraji,

Rasheed

2023

IOP Conf. Ser.: Earth Environ. Sci.

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“…In addition, arithmetical average (M), Standard deviation (SD), Least Significant Difference (L.S.D. ), Pearson Correlation Coefficient (R) and P Value from Pearson (R) of all the values under testing have been analysed [31][32][33][34][35].…”

Section: Discussionmentioning

confidence: 99%

A study of the Characteristics of Wastewater on the Euphrates River in Iraq

Hussein,

Al-Darraji,

Rasheed

et al. 2023

IOP Conf. Ser.: Earth Environ. Sci.

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Heavy metal toxicity and persistence are becoming major issues for people. These heavy metals mostly gather in wastewater from effluents released by different industries. The effectiveness of hazardous metal particle removal is currently just one recent trend in research; another is the efficient re-use of these particles as catalysts. The study was conducted for five sites on the Euphrates River in Anbar Governorate, western Iraq (Al Muḩammadī, Al-Khalidiya, Al-Habbaniya, Al-Saklawiya, Amirya Al-Falluja) with four stations for each site (the beginning of the estuary, after the estuary and before the estuary) and for four seasons (Summer, Autumn, Winter and Spring) from October 2021 to October 2022 to study spatial and temporal variation on the physical and chemical properties of the Euphrates River water in these locations. Sampling sites on the Euphrates River were selected based on these sites of waste, pollutants and heavy metal components that may flow into the river without environmental control. So, the study aimed at investigating the distribution of heavy metals (HMs: Manganese (Mn), Iron (Fe), Nickel (Ni), Copper (Cu), Lead (Pb), Cadmium (Cd)) in the sediments of the river for five sites in the west of Iraq. In the edge of the river (water) the Hardness, Salinity, algaes have been examined and for (sediments) the compounds (nitrite (NO2) and Sulfate (SO4)) and HMs concentration were measured too, and a qualitative study was conducted during the different seasons and sites. 79 types of algae were identified and some species prevailed in all studied sites. The quantitative study showed an increase in the number of algae species indicative of pollution in the sites in each station (the beginning, before and after the estuary), which confirms that these sites are affected by the untreated sewage pollutants thrown into the Euphrates River in those sites. The average concentrations of HMs and compounds in the sediments were as follows: SO4> NO2>Mn>Fe>Cu>Ni>Pb>Cd. The analysis showed that the pollution of cites by the HMs was as follows Al Muḩammadī, Al-Khalidiya, Al-Habbaniya, Al-Saklawiya, Amirya Al-Falluja cites concentrations are higher in sediments.

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“…Along with finite element techniques, FDM are one of the most frequently used ways for numerical solution of PDEs nowadays. At present, several methods are used to solve nonlinear equations [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40].…”

mentioning

confidence: 99%

The conjugate gradient approach to solve two dimensions linear elliptic boundary value equations as a prototype of the reaction diffusion system

Shawki Jaber,

RASHEED,

Saidani

2024

AJEST

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This paper presents a numerical approach to solve the 2-dimensional reaction-diffusion problem, a crucial model in physics and chemistry, with applications ranging from pattern formation to material science. Focusing on addressing a stationary linear elliptic problem within a rectangular domain, boundary conditions are determined through a finite-difference formulation. The Conjugate-Gradient Method is employed for the numerical solution, facilitating efficient computation. Key findings are elucidated: Firstly, the grid size for the symmetric matrix A is intricately linked to a bijective function, enabling the transition of indices to grid points. Notably, the solution to this elliptic problem exhibits a concave-up profile. Secondly, various solvers such as the Conjugate Gradient, Gauss-Seidel, and Jacobi techniques are viable, with the Conjugate Gradient method chosen for its superior accuracy, especially when considering computational efficiency. Moreover, the relationship between grid size and solution accuracy is explored, revealing a proportional dependence. Refinement of the grid leads to increased iteration counts but reduced implementation time, owing to the linearity of the function . The convergence criterion ensures high accuracy in solutions, as demonstrated in the provided figures.

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Orthogonal Boubaker-Turki polynomials algorithm for problems arising in engineering

Cited by 16 publications

References 17 publications

A study of Physicochemical Parameters, Heavy Metals and Algae in the Euphrates River, Iraq

A study of Physicochemical Parameters, Heavy Metals and Algae in the Euphrates River, Iraq

A study of the Characteristics of Wastewater on the Euphrates River in Iraq

The conjugate gradient approach to solve two dimensions linear elliptic boundary value equations as a prototype of the reaction diffusion system

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