Interval methods for verified integration of initial value problems (IVPs) for ODEs have been used for more than 40 years. For many classes of IVPs, these methods have the ability to compute guaranteed error bounds for the flow of an ODE, where traditional methods provide only approximations to a solution. Overestimation, however, is a potential drawback of verified methods. For some problems, the computed error bounds become overly pessimistic, or integration even breaks down. The dependency problem and the wrapping effect are particular sources of overestimations in interval computations. Berz (see [1]) and his co-workers have developed Taylor model methods, which extend interval arithmetic with symbolic computations. The latter is an effective tool for reducing both the dependency problem and the wrapping effect. By construction, Taylor model methods appear particularly suitable for integrating nonlinear ODEs. In this paper, we analyze Taylor model based integration of ODEs and compare Taylor model with traditional enclosure methods for IVPs for ODEs. More advanced Taylor model integration methods are discussed in the algorithm (1). For clarity, we summarize the major steps of the naive Taylor model method as algorithm 1.
The current study aims at identifying the impact of using learning acceleration model on the achievement of mathematics for third intermediategrade students. Forachieving this, the researchers chose the School (Al-Kholood Secondary School for Girls) affiliated to the General Directorate of Babylon Education / Hashemite Education Department for the academic year (2021/2021), The sample reached to (70) female students from the third intermediate grade, with (35) female students for each of the two research groups. The two researchers prepared an achievement test consisting of (25) objective items of multiple choice type, The psychometric properties of the test were confirmed, and after the completion of the experiment, the achievement test wa
... Show MoreIn the present study, activated carbon supported metal oxides was prepared for thiophene removal from model fuel (Thiophene in n-hexane) using adsorptive desulfurization technique. Commercial activated carbon was loaded individually with copper oxide in the form of Cu2O/AC. A comparison of the kinetic and isotherm models of the sorption of thiophene from model fuel was made at different operating conditions including adsorbent dose, initial thiophene concentration and contact time. Various adsorption rate constants and isotherm parameters were calculated. Results indicated that the desulfurization was enhanced when copper was loaded onto activated carbon surface. The highest desulfurization percent for Cu2O/AC and o
... Show MoreSurface water samples from different locations within Tigris River's boundaries in Baghdad city have been analyzed for drinking purposes. Correlation coefficients among different parameters were determined. An attempt has been made to develop linear regression equations to predict the concentration of water quality constituents having significant correlation coefficients with electrical conductivity (EC). This study aims to find five regression models produced and validated using electrical conductivity as a predictor to predict total hardness (TH), calcium (Ca), chloride (Cl), sulfate (SO4), and total dissolved solids (TDS). The five models showed good/excellent prediction ability of the parameters mentioned above, which is a very
... Show MoreThe hydrological process has a dynamic nature characterised by randomness and complex phenomena. The application of machine learning (ML) models in forecasting river flow has grown rapidly. This is owing to their capacity to simulate the complex phenomena associated with hydrological and environmental processes. Four different ML models were developed for river flow forecasting located in semiarid region, Iraq. The effectiveness of data division influence on the ML models process was investigated. Three data division modeling scenarios were inspected including 70%–30%, 80%–20, and 90%–10%. Several statistical indicators are computed to verify the performance of the models. The results revealed the potential of the hybridized s
... Show MoreThe research aims at identifying The Effect of Woods model in the Acquisition of Grammatical Concepts on students at the Sixth Primary. The total number of students is (49) male and female. students are distributed in two groups . The First group is the experimental group which is taught the( Woods Model) and it is (25) students . The second group is the control group which is taught according to the traditional method of teaching and it is (24) students . The researcher has matched between the two groups by the following variables : the age (in months), their intelligence, their parents, academic level of education . The research has constructed multiple choice test of (20) items . The reliability of The test has been calculated and it
... Show MoreThis paper discussed the solution of an equivalent circuit of solar cell, where a single diode model is presented. The nonlinear equation of this model has suggested and analyzed an iterative algorithm, which work well for this equation with a suitable initial value for the iterative. The convergence of the proposed method is discussed. It is established that the algorithm has convergence of order six. The proposed algorithm is achieved with a various values of load resistance. Equation by means of equivalent circuit of a solar cell so all the determinations is achieved using Matlab in ambient temperature. The obtained results of this new method are given and the absolute errors is demonstrated.
The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.
Abstract
The current research aims to identify the effect of using a model of generative learning in the achievement of first-middle students of chemical concepts in science. The researcher adopted the null hypothesis, which is there is no statistically significant difference at the level (0.05) between the mean scores of the experimental group who study using the generative learning model and the average scores of the control group who study using the traditional method in the chemical concepts achievement test. The research consisted of (200) students of the first intermediate at Al-Farqadin Intermediate School for Boys affiliated with the Directorate of General Education in Baghdad Governorate / Al-Karkh 3 wit
... Show MoreThis paper focuses on developing a self-starting numerical approach that can be used for direct integration of higher-order initial value problems of Ordinary Differential Equations. The method is derived from power series approximation with the resulting equations discretized at the selected grid and off-grid points. The method is applied in a block-by-block approach as a numerical integrator of higher-order initial value problems. The basic properties of the block method are investigated to authenticate its performance and then implemented with some tested experiments to validate the accuracy and convergence of the method.