In this paper we use non-polynomial spline functions to develop numerical methods to approximate the solution of 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of these method, and to compare the computed results with other known methods.

In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth

A new tool geometry was used to achieve friction stir spot welding (FSSW) in which the shoulder was designed separately from the rotating pin, and in order to examine weldment strength through the modified tool, a lap joints of AA2024 aluminum alloy plate 1 mm thick were welded successfully by using 6 mm pin diameter and varying process parameters (rotational speeds, tool nose geometry, and depth of tool penetration in the lower welded plate). Experimental tests indicate that the maximum average tensile shear load was 3100 N at the best selected condition. Microstructure examination and micro hardness test along the spot zones were investigated as well as measuring pin penetration load. Visual inspection of the welded spot surface shows a g

The removal of congo red (CR) is a critical issue in contemporary textile industry wastewater treatment. The current study introduces a combined electrochemical process of electrocoagulation (EC) and electro-oxidation (EO) to address the elimination of this dye. Moreover, it discusses the formation of a triple composite of Co, Mn, and Ni oxides by depositing fixed salt ratios (1:1:1) of these oxides in an electrolysis cell at a constant current density of 25 mA/cm2. The deposition ended within 3 hours at room temperature. X-ray diffractometer (XRD), field emission scanning electron microscopy (FESEM), atomic force microscopy (AFM), and energy dispersive X-ray (EDX) characterized the structural and surface morphology of the multi-oxide sedim

The aim of present study is to determine the optimum parameters of friction stir welding process and known the most important parameter along with percentage contribution of each parameter which effect on tensile strength and joint efficiency of FS welded joint of  dissimilar aluminum alloys AA2024-T3 and AA7075-T73 of 3 mm thick plates by applied specific number of experiments using Taguchi method .AA2024 was placed on the advancing side and AA7075 on the retreating side. FSW was achieved under three different rotation speeds (898, 1200 and 1710) rpm, three different welding speeds (20, 45 and 69) mm\min , three different pin profiles (cylindrical, threaded cylindrical and cone) and tool tilt angle 2^◦. Taguchi method w

Abstract The surface of kaolin was diagnosed by an AFM and the results were shown The height of the highest peak reached by a quantity of Kaolin ‎surface is 2.5 µm, the granules, and their diameter with an average diameter of 666.1nm. Using Kaolin's adsorption properties, erythrosine was removed of its aqueous solution. It was determined that the maximal dye adsorption ranged 36.53–40.61%. ‎‎‎‎The results of using the Freundlich, Langmuir, and Temkin adsorption isotherms revealed that at temperatures of (298,308,318) K, the Freundlich model was followed, the Langmuir model did not match, and the Temkin model could only be partially applied. There is also physical adsorption. One of the three kinetic models of the

To obtain the approximate solution to Riccati matrix differential equations, a new variational iteration approach was ‎proposed, which is suggested to improve the accuracy and increase the convergence rate of the approximate solutons to the ‎exact solution. This technique was found to give very accurate results in a few number of iterations. In this paper, the ‎modified approaches were derived to give modified solutions of proposed and used and the convergence analysis to the exact ‎solution of the derived sequence of approximate solutions is also stated and proved. Two examples were also solved, which ‎shows the reliability and applicability of the proposed approach. ‎

The aim of this paper is to present the numerical method for solving linear system of Fredholm integral equations, based on the Haar wavelet approach. Many test problems, for which the exact solution is known, are considered. Compare the results of suggested method with the results of another method (Trapezoidal method). Algorithm and program is written by Matlab vergion 7.