In this paper we use Bernstein polynomials for deriving the modified Simpson's 3/8 , and the composite modified Simpson's 3/8 to solve one dimensional linear Volterra integral equations of the second kind , and we find that the solution computed by this procedure is very close to exact solution.
In the present work, Response Surface Methodology (RSM) was utilized to optimize process variables and find the best circumstances for indirect electrochemical oxidation of mimicked wastewater to remove phenol contaminants using prepared ternary composite electrode. The electrodeposition process is used for the synthesis of a ternary composite electrode of Mn, Co, and Ni oxides. The selected concentrations of metal salts of these elements were 0.05, 0.1, and 1.5 M, with constant molar ratio, current density, and electrolysis time of 1:1:1, 25 mA/cm2, and 2 h. Interestedly, the gathered Mn-Co-Ni oxides were deposited at both the anode and cathode. X-ray diffraction (XRD) and scanning electron microscopy (SEM) facilitated the qualitative char
... Show MoreThe paper is devoted to solve nth order linear delay integro-differential equations of convolution type (DIDE's-CT) using collocation method with the aid of B-spline functions. A new algorithm with the aid of Matlab language is derived to treat numerically three types (retarded, neutral and mixed) of nth order linear DIDE's-CT using B-spline functions and Weddle rule for calculating the required integrals for these equations. Comparison between approximated and exact results has been given in test examples with suitable graphing for every example for solving three types of linear DIDE's-CT of different orders for conciliated the accuracy of the results of the proposed method.
In this effort, we define a new class of fractional analytic functions containing functional parameters in the open unit disk. By employing this class, we introduce two types of fractional operators, differential and integral. The fractional differential operator is considered to be in the sense of Ruscheweyh differential operator, while the fractional integral operator is in the sense of Noor integral. The boundedness and compactness in a complex Banach space are discussed. Other studies are illustrated in the sequel.
Composite materials are widely used in the engineered assets as aerospace structures, marine and air navigation owing to their high strength/weight ratios. Detection and identification of damage in the composite structures are considered as an important part of monitoring and repairing of structural systems during the service to avoid instantaneous failure. Effective cost and reliability are essential during the process of detecting. The Lamb wave method is an effective and sensitive technique to tiny damage and can be applied for structural health monitoring using low energy sensors; it can provide good information about the condition of the structure during its operation by analyzing the propagation of the wave in the
... Show MoreDue to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems
witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich
method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authors’
knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear
Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this
important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by
applying the well-known Newton-Kantorovich method. Also, to show the efficiency of appl
In this paper, the finite element method is used to study the dynamic behavior of the damaged rotating composite blade. Three dimensional, finite element programs were developed using a nine node laminated shell as a discretization element for the blade structure (the same element type is used for damaged and non-damaged structure). In this analysis the initial stress effect (geometric stiffness) and other rotational effects except the carioles acceleration effect are included. The investigation covers the effect speed of rotation, aspect ratio, skew angle, pre-twist angle, radius to length, layer lamination and fiber orientation of composite blade. After modeling a non-damaged rotating composite blade, the work procedure was to ap
... Show MoreThe Boltzmann equation has been solved using (EEDF) package for a pure sulfur hexafluoride (SF6) gas and its mixtures with buffer Helium (He) gas to study the electron energy distribution function EEDF and then the corresponding transport coefficients for various ratios of SF6 and the mixtures. The calculations are graphically represented and discussed for the sake of comparison between the various mixtures. It is found that the various SF6 – He content mixtures have a considerable effect on EEDF and the transport coefficients of the mixtures