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.
Generalized Additive Model has been considered as a multivariate smoother that appeared recently in Nonparametric Regression Analysis. Thus, this research is devoted to study the mixed situation, i.e. for the phenomena that changes its behaviour from linear (with known functional form) represented in parametric part, to nonlinear (with unknown functional form: here, smoothing spline) represented in nonparametric part of the model. Furthermore, we propose robust semiparametric GAM estimator, which compared with two other existed techniques.
This work addressed the assignment problem (AP) based on fuzzy costs, where the objective, in this study, is to minimize the cost. A triangular, or trapezoidal, fuzzy numbers were assigned for each fuzzy cost. In addition, the assignment models were applied on linguistic variables which were initially converted to quantitative fuzzy data by using the Yager’sorankingi method. The paper results have showed that the quantitative date have a considerable effect when considered in fuzzy-mathematic models.
This study aims to numerically simulate the flow of the salt wedge by using computational fluid dynamics, CFD. The accuracy of the numerical simulation model was assessed against published laboratory data. Twelve CFD model runs were conducted under the same laboratory conditions. The results showed that the propagation of the salt wedge is inversely proportional to the applied freshwater discharge and the bed slope of the flume. The maximum propagation is obtained at the lowest discharge value and the minimum slope of the flume. The comparison between the published laboratory results and numerical simulation shows a good agreement. The range of the relative error varies between 0 and 16% with an average of 2% and a roo
... Show MoreIn this paper has been building a statistical model of the Saudi financial market using GARCH models that take into account Volatility in prices during periods of circulation, were also study the effect of the type of random error distribution of the time series on the accuracy of the statistical model, as it were studied two types of statistical distributions are normal distribution and the T distribution. and found by application of a measured data that the best model for the Saudi market is GARCH (1,1) model when the random error distributed t. student's .
Objective: To generate a model that conceptualizes the phenomenon of health promotion and its related factors.
Methodology: A grounded theory methodology is used as qualitative method to explore the health promotion as
phenomenon of interest and its other related factors from the perspectives of specialists in this field. The study is
carried out from January 2002 through September 2004. A sample of (20) specialists in health sciences are
selected and interviewed as experts in the area of health promotion. The investigators conducted intensive and
structured interviews with the specialists to collect the data. These interviews were transcribed verbatim,
analyzed and interpreted.
Results: Findings of the study indicat
In the current study, haemoglobin analytes dissolved in a special buffer (KH2PO4(1M), K2HPO4(1M)) with pH of 7.4 were used to record absorption spectra measurements with a range of concentrations from (10-8 to 10-9) M and an absorption peak of 440nm using Broadband Cavity Enhanced Absorption Spectroscopy (BBCEAS) which is considered a simple, low cost, and robust setup. The principle work of this technique depends on the multiple reflections between the light source, which is represented by the Light Emitting Diode 3 W, and the detector, which is represented by the Avantes spectrophotomer. The optical cavity includes two high reflectivity ≥99% dielectric mirrors (dia
... Show MoreThe result of a developed mathematical model for predicting the design
parameters of the fiber Raman amplifier (FRA) are demonstrated. The amplification
parameters are tested at different pump power with different fiber length. Recently,
the FRA employed in optical communication system to increase the repeater distance
as will as the capacity of the communication systems. The output results show, that
high Raman gain can be achieved by high pumping power, long effective area that
need to be small for high Raman gain. High-stimulated Raman gain coefficient is
recommended for high Raman amplifier gain, the low attenuation of the pump and the
transmitted signal in the fiber lead to high Raman gain.
Every researcher must say that the world in continually progress toward the best and that
the Arab and Islamic civilization had produced much of systems and virtuous educational
practices which raised from Islamic heritage. This nation was not isolated from external
world, but it was made a clear active for promote the banner of other nations which entered
under her influence to promote Islamic banner and Muslims. Consequently also Muslims are
affected and influenced, this resulted a clear impact in the civilization and educational
ideology especially in the contemporary teaching methods.
A new efficient Two Derivative Runge-Kutta method (TDRK) of order five is developed for the numerical solution of the special first order ordinary differential equations (ODEs). The new method is derived using the property of First Same As Last (FSAL). We analyzed the stability of our method. The numerical results are presented to illustrate the efficiency of the new method in comparison with some well-known RK methods.