This paper is dealing with non-polynomial spline functions "generalized spline" to find the approximate solution of linear Volterra integro-differential equations of the second kind and extension of this work to solve system of linear Volterra integro-differential equations. The performance of generalized spline functions are illustrated in test examples

An efficient combination of Adomian Decomposition iterative technique coupled with Laplace transformation to solve non-linear Random Integro differential equation (NRIDE) is introduced in a novel way to get an accurate analytical solution. This technique is an elegant combination of theLaplace transform, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has also been established that (LT

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

This study focuses on studying an oscillation of a second-order delay differential equation. Start work, the equation is introduced here with adequate provisions. All the previous is braced by theorems and examplesthat interpret the applicability and the firmness of the acquired provisions

The current research aims to prepare a proposed Programmebased sensory integration theory for remediating some developmental learning disabilities among children, researchers prepared a Programme based on sensory integration through reviewing studies related to the research topic that can be practicedby some active teaching strategies (cooperative learning, peer learning, Role-playing, and educational stories). The Finalformat consists of(39) training sessions.

Transportability refers to the ease with which people, goods, or services may be transferred. When transportability is high, distance becomes less of a limitation for activities. Transportation networks are frequently represented by a set of locations and a set of links that indicate the connections between those places which is usually called network topology. Hence, each transmission network has a unique topology that distinguishes its structure. The most essential components of such a framework are the network architecture and the connection level. This research aims to demonstrate the efficiency of the road network in the Al-Karrada area which is located in the Baghdad city. The analysis based on a quantitative evaluation using graph th