In this paper Volterra Runge-Kutta methods which include: method of order two and four will be applied to general nonlinear Volterra integral equations of the second kind. Moreover we study the convergent of the algorithms of Volterra Runge-Kutta methods. Finally, programs for each method are written in MATLAB language and a comparison between the two types has been made depending on the least square errors.

In this paper the modified trapezoidal rule is presented for solving Volterra linear Integral Equations (V.I.E) of the second kind and we noticed that this procedure is effective in solving the equations. Two examples are given with their comparison tables to answer the validity of the procedure.

This paper demonstrates an experimental and numerical study aimed at comparing the influence of openings of different configurations on the flexural behavior of reinforced concrete gable roof beams. The experimental program consisted of testing six simply supported gable beams subjected to mid-point concentrated load. The variable which has been investigated in this work was opening's configuration (quadrilateral or circular) with the same upper and lower chords depth. The results indicate improvement in the beams’ flexural behavior when circular openings were used compared with that of quadrilateral openings, represented by an increase in ultimate load capacity and a decrease in deflection at the service limit. Also, there was an

Nowadays, the use of recycled waste construction materials instead of aggregates is becoming popular in construction owing to its environmental benefits. This paper presents an experimental and analytical campaign to study the behavior of axially loaded columns constructed from recycled aggregates. The latter was used instead of natural aggregates, and they were collected from the waste of previous concrete constructions. Different concrete mixtures made from varying amounts of recycled aggregates ranged from 0 to 50% of the total coarse aggregate were conducted to achieve 28 MPa. The effect of steel fibers is another investigated variable with volumes ranged from 0 to 2% concerning concrete’s mixture. The experimental

In line with the advancement of hardware technology and increasing consumer demands for new functionalities and innovations, software applications grew tremendously in term of size over the last decade. This sudden increase in size has a profound impact as far as testing is concerned. Here, more and more unwanted interactions among software systems components, hardware, and operating system are to be expected, rendering increased possibility of faults. To address this issue, many useful interaction-based testing techniques (termed t-way strategies) have been developed in the literature. As an effort to promote awareness and encourage its usage, this chapter surveys the current state-of-the-art and reviews the state-of-practices in t

In line with the advancement of hardware technology and increasing consumer demands for new functionalities and innovations, software applications grew tremendously in term of size over the last decade. This sudden increase in size has a profound impact as far as testing is concerned. Here, more and more unwanted interactions among software systems components, hardware, and operating system are to be expected, rendering increased possibility of faults. To address this issue, many useful interaction-based testing techniques (termed t-way strategies) have been developed in the literature. As an effort to promote awareness and encourage its usage, this chapter surveys the current state-of-the-art and reviews the state-of-practices in t

The aim of this paper is to propose a reliable iterative method for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method. Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibits that this technique was compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations.

Geotechnical engineers have always been concerned with the stabilization of slopes. For this purpose,
various methods such as retaining walls, piles, and geosynthetics may be used to increase the safety factor of slopes prone to failure. The application of stone columns may also be another potential alternative for slope stabilization. Such columns have normally been used for cohesive soil improvement. Most slope analysis and design is based on deterministic approach i.e a set of single valued design parameter are adopted and a set of single valued factor of safety (FOS) is determined. Usually the FOS is selected in view of the understanding and knowledge of the material parameters, the problem geometry, the method of analysis and the

In modern hydraulic control systems, the trend in hydraulic power applications is to improve efficiency and performance. “Proportional valve” is generally applied to pressure, flow and directional-control valves which continuously convert a variable input signal into a smooth and proportional hydraulic output signal. It creates a variable resistance (orifice) upstream and downstream of a hydraulic actuator, and is meter in/meter out circuit and hence pressure drop, and power losses are inevitable. If velocity (position) feedback is used, flow pattern control is possible. Without aforementioned flow pattern, control is very “loose” and relies on “visual” feed back by the operator. At this point, we should examine how this valv