The method of operational matrices is based on the Bernoulli and Shifted Legendre polynomials which is used to solve the Falkner-Skan equation. The nonlinear differential equation converting to a system of nonlinear equations is solved using Mathematica®12, and the approximate solutions are obtained. The efficiency of these methods was studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as increases. Moreover, the obtained approximate solutions are compared with the numerical solution obtained by the fourth-order Runge-Kutta method (RK4), which gives a good agreement.
The rapid success and the field dilation of Daish organization in both Iraq and Syria make academic institutes and research centers to pay attention to its propaganda means to gain its public opinion, and to further investigation about new methods employed by this organization to disseminate its messages to the public, particularly young people in large areas of the world. This organization uses traditional propaganda techniques on psychological war and its levels, social network sites and platforms that are distributed online. This study seeks to expose more persuasive methods used by the organization to gain multiple classes of society and to disseminate its extremist ideological thoughts. It also studies the psychological operation an
... Show MoreOscillation criterion is investigated for all solutions of the first-order linear neutral differential equations with positive and negative coefficients. Some sufficient conditions are established so that every solution of eq.(1.1) oscillate. Generalizing of some results in [4] and [5] are given. Examples are given to illustrated our main results.
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
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.
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
... Show MoreThe issue, the existence of God Almighty, and the creativity of the universes including the whale, and assets and how diversified, and faith in him and his lordship and divinity, is a delicate issue, and very important and dangerous, and it occupied human thought old and new, and still occupy it until God takes the land and on it. Many complex issues of thought, behavior, and ethics have resulted in the belief of many communities in the existence of the Almighty, having ruled their minds, depicting their beliefs and distancing their thoughts about slippage and abuse. When they looked at the wonders of creatures and the minutes of the assets, they thought about the planetary and astronomical motion systems. His existence was denied by ath
... Show MorePrediction of daily rainfall is important for flood forecasting, reservoir operation, and many other hydrological applications. The artificial intelligence (AI) algorithm is generally used for stochastic forecasting rainfall which is not capable to simulate unseen extreme rainfall events which become common due to climate change. A new model is developed in this study for prediction of daily rainfall for different lead times based on sea level pressure (SLP) which is physically related to rainfall on land and thus able to predict unseen rainfall events. Daily rainfall of east coast of Peninsular Malaysia (PM) was predicted using SLP data over the climate domain. Five advanced AI algorithms such as extreme learning machine (ELM), Bay
... Show MoreIn this paper Hermite interpolation method is used for solving linear and non-linear second order singular multi point boundary value problems with nonlocal condition. The approximate solution is found in the form of a rapidly convergent polynomial. We discuss behavior of the solution in the neighborhood of the singularity point which appears to perform satisfactorily for singular problems. The examples to demonstrate the applicability and efficiency of the method have been given.
This study is dedicated to solving multicollinearity problem for the general linear model by using Ridge regression method. The basic formulation of this method and suggested forms for Ridge parameter is applied to the Gross Domestic Product data in Iraq. This data has normal distribution. The best linear regression model is obtained after solving multicollinearity problem with the suggesting of 10 k value.