In this paper, third order non-polynomial spline function is used to solve 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of this method, and to compare the computed results with other known methods.

Environmental pollution is experiencing an alarming surge within the global ecosystem, warranting urgent attention. Among the significant challenges that demand immediate resolution, effective treatment of industrial pollutants stands out prominently, which for decades has been the focus of most researchers for sustainable industrial development aiming to remove those pollutants and recover some of them. The liquid membrane (LM) method, specifically electromembrane extraction (EME), offers promise. EME deploys an electric field, reducing extraction time and energy use while staying eco-friendly. However, there's a crucial knowledge gap. Despite strides in understanding and applying EME, optimizing it for diverse industrial pollutant

Environmental pollution is experiencing an alarming surge within the global ecosystem, warranting urgent attention. Among the significant challenges that demand immediate resolution, effective treatment of industrial pollutants stands out prominently, which for decades has been the focus of most researchers for sustainable industrial development aiming to remove those pollutants and recover some of them. The liquid membrane (LM) method, specifically electromembrane extraction (EME), offers promise. EME deploys an electric field, reducing extraction time and energy use while staying eco-friendly. However, there's a crucial knowledge gap. Despite strides in understanding and applying EME, optimizing it for diverse industrial pollutant

The increasing discharge of dye-containing wastewater has become a serious environmental problem, requiring efficient and sustainable treatment technologies. In this study, poultry litter–derived biochar (BC) was prepared via pyrolysis at 550 °C and subsequently modified with chitosan to produce a composite adsorbent (BC/CS) for the removal of Congo Red (CR) from aqueous solutions. The materials were characterized using SEM, BET, XRD, FTIR, and XPS analyses. BET results showed that chitosan modification slightly decreased the specific surface area from 8.28 to 8.18 m²/g and pore volume from 0.035 to 0.030 cm³ /g, while introducing abundant amine and hydroxyl functional groups on the surface. Maximum adsorption occurred at pH 3, w

   Adsorption of lead ions from wastewater by native agricultural waste, precisely tea waste. After the activation and carbonization of tea waste, there was a substantial improvement in surface area and other physical characteristics which include density, bulk density, and porosity. FTIR analysis indicates that the functional groups in tea waste adsorbent are aromatic and carboxylic. It can be concluded that the tea waste could be a good sorbent for the removal of Lead ions from wastewater. Different dosages of the adsorbents were used in the batch studies. A random series of experiments indicated a removal degree efficiency of lead reaching (95 %) at 5 ppm optimum concentration, with adsorbents R² =97.75% for tea. Three mo

In this study, mesoporous silica (MPS) is made using the sol-gel method from a cheap source (Na2SiO3) using the surfactant hydroxycetyl hydroxyethyl dimonium chloride as a template. The task is the adsorption-based removal of the medication metoprolol (MP) at concentrations between 10 and 50 ppm. Variables such as: contact time, dose of adsorbent, starting concentration of adsorbate, and adsorption temperature were studied which show the equilibrium time and adsorbent dose are 40 min and 0.05 g respectively. The Langmuir, Freundlich, Temkin, and Dubinin-Radushkevich isotherm models were fitted to the data obtained from the experiments. Comparing the outcomes showed that, of the four investigated isotherm models, the Freundlich equation m

Water-based drilling fluids (WBDFs) are the industry-preferred medium for drilling reactive shale formations, yet they remain susceptible to shale swelling, fluid invasion, and cuttings dispersion—all of which compromise wellbore stability. Although oil-based fluids (OBFs) provide effective shale inhibition, their high cost and adverse environmental profile limit their use. Nanoparticles (NPs) derived from waste feedstocks offer a low-cost, environmentally responsible alternative for enhancing WBDF performance, but no prior study has simultaneously evaluated both waste-derived SiO2 and Al2O2 NPs within a single WBDF system. This study synthesised SiO2 NPs from Halfaya bentonite clay waste and Al2O2 NPs from recycled aluminium scrap, char

 A problem of solid waste became in the present day common global problem among all countries, whether developing or developed countries, and can say that no country in the world today is immuning from this dilemma which must find appropriate solutions. The problem has reached a stage that can not ignore or delay, but has became a daily problem occupies the minds of ecologists, economists and politicians took occupies center front in the lists of  priorities for the countries in terms of finding solutions to the rapid scientific and radical them. and that transport costs constitute an important component of total costs borne by the municipal districts in the process of disposal of solid waste, so any improvement in the