In our article, three iterative methods are performed to solve the nonlinear differential equations that represent the straight and radial fins affected by thermal conductivity. The iterative methods are the Daftardar-Jafari method namely (DJM), Temimi-Ansari method namely (TAM) and Banach contraction method namely (BCM) to get the approximate solutions. For comparison purposes, the numerical solutions were further achieved by using the fourth Runge-Kutta (RK4) method, Euler method and previous analytical methods that available in the literature. Moreover, the convergence of the proposed methods was discussed and proved. In addition, the maximum error remainder values are also evaluated which indicates that the propo

This paper considers approximate solution of the hyperbolic one-dimensional wave equation with nonlocal mixed boundary conditions by improved methods based on the assumption that the solution is a double power series based on orthogonal polynomials, such as Bernstein, Legendre, and Chebyshev. The solution is ultimately compared with the original method that is based on standard polynomials by calculating the absolute error to verify the validity and accuracy of the performance.

     The primary objective of the current paper is to suggest and implement effective computational methods (DECMs) to calculate analytic and approximate solutions to the nonlocal one-dimensional parabolic equation which is utilized to model specific real-world applications. The powerful and elegant methods that are used orthogonal basis functions to describe the solution as a double power series have been developed, namely the Bernstein, Legendre, Chebyshev, Hermite, and Bernoulli polynomials. Hence, a specified partial differential equation is reduced to a system of linear algebraic equations that can be solved by using Mathematica®12. The techniques of effective computational methods (DECMs) have been applied to solve some s

A new benzylidene derivative, namely N-benzylidene-5-phenyl-1,3,4-thiadiazol-2-amine (BPTA), has been synthesized and instrumentally confirmed with Elemental Analysis (CHN), Nuclear Magnetic Resonance (NMR), and Fourier Transform Infrared Spectroscopy (FT-IR). Titanium Dioxide (TiO2) nanoparticles (NPs) were synthesized and characterized by X-ray. The mutualistic complementary dependence of BPTA with TiO2 nanoparticles as anti-corrosive inhibitor on mild steel (MS) in 1.0 M hydrochloric acid has been tested at various concentrations and various temperatures. The methodological work was achieved by gravimetric measurement methods complemented with surface analysis. The synthesized inhibitor concentrations were 0.1 mM to 0.5 mM and the temper

A novel robust finite time disturbance observer (RFTDO) based on an independent output-finite time composite control (FTCC) scheme is proposed for an air conditioning-system temperature and humidity regulation. The variable air volume (VAV) of the system is represented by two first-order mathematical models for the temperature and humidity dynamics. In the temperature loop dynamics, a RFTDO temperature (RFTDO-T) and an FTCC temperature (FTCC-T) are designed to estimate and reject the lumped disturbances of the temperature subsystem. In the humidity loop, a robust output of the FTCC humidity (FTCC-H) and RFTDO humidity (RFTDO-H) are also designed to estimate and reject the lumped disturbances of the humidity subsystem. Based on Lyapunov theo

The study seeks the relationship between the mathematical-procedural Knowledge and the logical-mathematical intelligence among students at the third stage in mathematics department. To this end, three questions were arisen: what is the level of mathematical-procedural Knowledge among the third stage students in mathematics department regarding their gender? Do male or female students have more logical-mathematical intelligence and are there significant differences base on their gender? What kind of correlation is between the level of mathematical-procedural Knowledge and the logical-mathematical intelligence of male and female students in the third stage in the mathematics department? A sample of (75) male and female students at the thir

Photodynamic Action (PDA) by using appropriate wavelength of irradiation conjugated with porphyrin derivatives is a powerful mechanism of tumor destruction. Hematoporphyrin derivative has been shown to selectively localize in neoplastic cells and then cause destruction of them by generation of singlet oxygen when activated by low power He-Ne laser. Light which used in this study has been emitting from this laser has a wavelength equal to 632.8 nm (red light). Doses of laser had been varied from 3.6 J/cm2 to 14.4 J/cm2 . The beam of laser adjusted with a modified tissue culture plate. Cell lines had exposed to Hematoporphyrin D (HpD) for 24 hours before Laser exposure, their concentrations were varied from 5 µg/ml to 80 µg/ml. Resu

     New chelating ligand derived from triazole and its complexes with metal ions Rhodium, Platinum and Gold were synthesized. Through a copper (I)-catalyzed click reaction, the ligand produced 1,3-dipolar cycloaddition between 2,6-bis((prop-2-yn-1-yloxy) methyl) pyridine and 1-azidododecane. All structures of these new compounds were rigorously characterized in the solid state using spectroscopic techniques like: 1HNMR, 13CNMR, Uv-Vis, FTIR, metal and elemental analyses, magnetic susceptibility and conductivity measurements at room temperature, it was found that the ligand acts as a penta and tetradentate chelate through N3O2, N2O2, and the geometry of the new complexes are identified as octahedral for (Rh & Pt) complexes a