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.
Suitability of groundwater for irrigation depends upon many constrains factors, these factors depend upon the dissolved salts during the flow of the recharge of the groundwater beside the aquifer constituents itself, from these factors (EC, SO4-2, Cl-, Na%, and SAR) .The spatial distribution of each constrain factor may show discrepancy from the another, so it is not possible to depend upon one factor. The aim of this work is to present a classification of the groundwater quality for agriculture including all the mentioned five factors, by using Arc GIS which provides tools to serve a purpose to create conceptual model for solving spatial problems. A set of conceptual steps used to build a model for suitability map of groundwater for irr
... Show MoreIn the present work, the nuclear shell model with Hartree–Fock (HF) calculations have been used to investigate the nuclear structure of 24Mg nucleus. Particularly, elastic and inelastic electron scattering form factors and transition probabilities have been calculated for low-lying positive and negative states. The sd and sdpf shell model spaces have been used to calculate the one-body density matrix elements (OBDM) for positive and negative parity states respectively. Skyrme-Hartree-Fock (SHF) with different parameterizations has been tested with shell model calculation as a single particle potential for reproducing the experimental data along with a harmonic oscillator (HO) and Woods-Saxo
... Show Moresingle and binary competitive sorption of phenol and p-nitrophenol onto clay modified with
quaternary ammonium (Hexadecyltrimethyl ammonium ) was investigated to obtain the
adsorption isotherms constants for each solutes. The modified clay was prepared from
blending of local bentonite with quaternary ammonium . The organoclay was characterized
by cation exchange capacity. and surface area. The results show that paranitrophenol is
being adsorbed faster than phenol . The experimental data for each solute was fitted well with
the Freundlich isotherm model for single solute and with the combination of Freundlich-
Langmuier model for binary system .
To study the striking perturbations of ionospheric Total Electron Content (TEC) before, during, and after the earthquake (M≥5) for earlier prediction to avoid calamities, ionospheric TEC data are taken by using red shift technique from two-frequencies GPS signals.. Tohoku earthquake on 11th March 2011 is chosen as case of our study (A magnitude M9.0 earthquake reported by the US Geological Survey gives its origin time at 05:46:23 UTC; the epicenter was located at 38.322oN, 142.369oE of the east coast of Honshu). The study was made 15 days before and 15 days after earthquake occurred over Japan at four different geographic positions, Kokubunji (35.7oN, 139.5oE), Wakkanai (45.2oN, 141.8oE), Yamagawa (31.2oN, 130.6oE) and Okinawa (26.7oN,
... Show MoreIntegration of laminar bubbling flow with heat transfer equations in a novel internal jacket airlift bioreactor using microbubbles technology was examined in the present study. The investigation was accomplished via Multiphysics modelling to calculate the gas holdup, velocity of liquid recirculation, mixing time and volume dead zone for hydrodynamic aspect. The temperature and internal energy were determined for heat transfer aspect.
The results showed that the concentration of microbubbles in the unsparged area is greater than the chance of large bubbles with no dead zones being observed in the proposed design. In addition the pressure, due to the recirculation velocity of liquid around the draft
... Show MoreThe Effect of the Addie and Shayer Model on the Achievement of Fifth Grade Students and their Attitudes towards History
- Ahmed Hashim Mohammed and Hadil Jassas Ali
University of Baghdad - College of Education for Women
Abstract
The current research aims to examine the effect of the Adi and Shayer model on the achievement of fifth-grade students and their attitudes toward history. To achieve the research objective, the researcher has adopted two null hypotheses. 1) there is no statistically significant difference at the level o
... Show MoreReservoir study has been developed in order to get a full interesting of the Nahr Umr formation in Ratawi oil field. Oil in place has been calculated for Nahr Umr which was 2981.37 MM BBL. Several runs have been performed to get matching between measured and calculated of oil production data and well test pressure. In order to get the optimum performance of Nahr Umr many strategies have been proposed in this study where vertical and horizontal wells were involved in addition to different production rates. The reservoir was first assumed to be developed with vertical wells only using production rate of (80000–125000) STB/day. The reservoir is also proposed to produce using horizontal wells besides vertical wells with pr
... Show MoreThis study aims to analyze the flow migration of individuals between Iraqi governorates using real anonymized data from Korek Telecom company in Iraq. The purpose of this analysis is to understand the connection structure and the attractiveness of these governorates through examining the flow migration and population densities. Hence, they are classified based on the human migration at a particular period. The mobile phone data of type Call Detailed Records (CDRs) have been observed, which fall in a 6-month period during COVID-19 in the year 2020-2021. So, according to the CDRs nature, the well-known spatiotemporal algorithms: the radiation model and the gravity model were applied to analyze these data, and they are turned out to be comp
... Show MoreA neutron induced deuteron emission spectra and double differential cross-sections (DDX), in 27Al (n, D) 26Mg, 51V (n, D)50Ti , 54Fe ( n, D)53Mn and 63Cu (n, D) 62Ni reactions, have been investigated using the phenomenological approach model of Kalbach. The pre-equilibrium stage of the compound nucleus formation is considered the main pivot in the discription of cross-section, while the equilibrium (pick up or knock out ) process is analyzed in the framework of the statistical theory of cluster reactions, Feshbach, Kerman, and Koonin (FKK) model. To constrain the applicable parameterization as much as possible and to assess the predictive power of these models, the calculated results have been compared with the experimental data and othe
... Show MoreThe adsorption behavior of congo red dye from its aqueous solutions was investigated onto natural and modified bauxite clays. Both bauxite and modified bauxite are primarily characterized by using, FTIR, SEM, AFM, and XRD. Several variables are studied as a function of adsorption including contact time, adsorbent weight, pH, ionic strength, particle size and temperature under batch adsorption technique. The absorbance of the solution before and after adsorption was measured spectrophotometrically. The equilibrium data fit with Langmuir model of adsorption and the linear regression coefficient R2 is found to be 0.9832 and 0.9630 for natural and modified bauxite respectively at 37.5°C which elucidate the best fitting isotherm model. The gene
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