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.

A non-polynomial spline (NPS) is an approximation method that relies on the triangular and polynomial parts, so the method has infinite derivatives of the triangular part of the NPS to compensate for the loss of smoothness inherited by the polynomial. In this paper, we propose polynomial-free linear and quadratic spline types to solve fuzzy Volterra integral equations (FVIE) of the 2nd kind with the weakly singular kernel (FVIEWSK) and Abel's type kernel. The linear type algorithm gives four parameters to form a linear spline. In comparison, the quadratic type algorithm gives five parameters to create a quadratic spline, which is more of a credit for the exact solution. These algorithms process kernel singularities with a simple techniqu

The flexible joint robot (FJR) typically experiences parametric variations, nonlinearities, underactuation, noise propagation, and external disturbances which seriously degrade the FJR tracking. This article proposes an adaptive integral sliding mode controller (AISMC) based on a singular perturbation method and two state observers for the FJR to achieve high performance. First, the underactuated FJR is modeled into two simple second-order fast and slow subsystems by using Olfati transformation and singular perturbation method, which handles underactuation while reducing noise amplification. Then, the AISMC is proposed to effectively accomplish the desired tracking performance, in which the integral sliding surface is designed to reduce cha

Consequence of thermal and concentration convection on peristaltic pumping of hyperbolic tangent nanofluid in a non‐uniform channel and induced magnetic field is discussed in this article. The brief mathematical modeling, along with induced magnetic field, of hyperbolic tangent nanofluid is given. The governing equations are reduced to dimensionless form by using appropriate transformations. Exact solutions are calculated for temperature, nanoparticle volume fraction, and concentration. Numerical technique is manipulated to solve the highly non‐linear differential equations. The roll of different variables is graphically analyzed in terms of concentration, temperature, volume fraction of nanoparticles, axial induced magnetic fie

The numerical resolve nonlinear system of Volterra integral equation of the second kind (NLSVIEK2) has been considered. The exponential function is used as the base function of the collocation method to approximate the resolve of the problem. Arithmetic epitome are performed which have already been solved by weighted residual manner,  Taylor manner and block- by- block(2, 3, 5).

In this research, some probability characteristics functions (probability density, characteristic, correlation and spectral density) are derived depending upon the smallest variance of the exact solution of supposing stochastic non-linear Fredholm integral equation of the second kind found by Adomian decomposition method (A.D.M)

The decorative supplements added are important factors in determining many decorative effects and how to implement them, whether in fabrics or fashion, and also work to determine the nature of perception for both the designer and the recipient and have a key role in shaping the human personality and determining his motives and emotional tendencies in the acquisition of fabrics and fashion and the vocabulary they carry A design that has certain connotations and symbols that gain its value from the effects it leaves on the physical formations of women. The problem of the research came with the following question (What are the decorative supplements and their role in the designs of fabrics and women’s fashion?) The research also dealt wit

The study of the concepts of "democracy" and "human rights" and their impact on development, has taken a prominent place in the context of general political and cultural concerns, or in specialized studies even though researchers and scholars do not agree on defining the concepts: Democracy, Human Rights, Development or deriving a global definition hindering them, and that because of the importance of this topic, which proceeds from a number of considerations standing in the forefront, of which:

First: What the world witnesses today in the first decade of this century of consecration of the unipolar theory, trying to give its concepts and perceptions through the law ((excessive force)) to the power of international

The problem of the study is to monitor the content presented in the Iraqi satellite channels to identify the nature of the ideas contained in these ads and to identify the values ​​carried by the creative strategies and ad campaigns that use. Where the satellite is one of the most important technological developments in the field of communications in the nineties and the ads in various forms and functions one of the contents provided by satellite channels where these channels are keen to direct their messages in particular and communication, in general, to address a certain audience and convince and influence in order to achieve certain purposes of the source Or the body from which it originates, especially those that result in an in