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.
Abstract
The issue of the protection of the environment is a shared responsibility between several destinations and sectors, and constitutes a main subject in which they can achieve sustainable development. In the sectors of government programs can be set up towards the establishment of the government sector to the green environment, so to be the implementati
... Show MoreThe topic of this research deals with an analytical study of the nature of the visual sent by the sculptural monument of the person of Christ around the world, the nature of this monument, the manner of its embodiment, the mechanism of reception for each of the societies that this monument addressed to them, how it was reflected on them, how it was reflected on them, and whether these works are related to their culture or not, I discussed this study All this, and the researcher has established theoretical research axes for the research according to the desired goal of this study, which is the definition of the mechanism of visual discourse of statues of Christ around the world and were as follows: (The first axis: the discourse and visua
... Show MoreThe study included three topics, the definition of the personality of Imam al-Bazazi, his scientific biography, his elders, his writings, his students and his death, selected issues of his weightiness related to purity, and the Imam al-Bazazi is Muhammad ibn Muhammad ibnShihabibn Yusuf, known in al-Kardari al-Hanafi al-Balzazi. The other doctrines, the author relied in his book on the sources of the previous scholars of the Hanafis, and make them the basis in his book, the author did not adopt the definitions of language and terminology, and rarely mention the evidence Shariah adopted by scientists in their opinions, and limited to mention only opinions, In front of the first issue spotlessly water user, and the second issue that sleep l
... Show MoreThe implicit pattern is one of the cultural patterns that are present in both the text and theatrical presentation and the reading of the implicit pattern cannot take place without cognitive references, whether audio or visual as well as historical references and the natural, social and psychological dimensions of communities and individuals.
The researcher, in this study, attempted to focus on the axis of the aesthetic preoccupations of the implicit pattern in the theatrical presentation and the definition of the implicit pattern. Methodologically speaking, the research problem focused on revealing the outlines and the main features in the aesthetic preoccupations that shape the i
... Show MoreThis paper presents an analytical study for the magnetohydrodynamic (MHD) flow of a generalized Burgers’ fluid in an annular pipe. Closed from solutions for velocity is obtained by using finite Hankel transform and discrete Laplace transform of the sequential fractional derivatives. Finally, the figures are plotted to show the effects of different parameters on the velocity profile.
This study discussed a biased estimator of the Negative Binomial Regression model known as (Liu Estimator), This estimate was used to reduce variance and overcome the problem Multicollinearity between explanatory variables, Some estimates were used such as Ridge Regression and Maximum Likelihood Estimators, This research aims at the theoretical comparisons between the new estimator (Liu Estimator) and the estimators
In recent years, non-oil primary balance indicator has been given considerable financial important in rentier state. It highly depends on this indicator to afford a clear and proper picture of public finance situation in term of appropriate and sustainability in these countries, due to it excludes the effect of oil- rental from compound of financial accounts which provide sufficient information to economic policy makers of how economy is able to create potential added value and then changes by eliminating one sided shades of economy. In Iraq, since, 2004, the deficit in value of this indicator has increased, due to almost complete dependence on the revenues of the oil to finance the budget and the obvious decline of the non-oil s
... Show MoreThis study aims to answer a significant problem of social sciences and philosophy: How do we construct an institutional reality such as diplomacy with an objective recognizable existence? The study assumes that the ability to build institutional reality is based on our biological capacity, as it takes different forms in all the institutions we construct. The study takes the theory of the American philosopher John Searle as an approach to examining the assumption. The study sums up important findings; cultures, although they share the biological capacity on which they produce institutional realities, differ in the form of the value standards on which the institutional realities are based. The study recommends the need of Arab social resea
... Show MoreThe behaviour of certain dynamical nonlinear systems are described in term as chaos, i.e., systems' variables change with the time, displaying very sensitivity to initial conditions of chaotic dynamics. In this paper, we study archetype systems of ordinary differential equations in two-dimensional phase spaces of the Rössler model. A system displays continuous time chaos and is explained by three coupled nonlinear differential equations. We study its characteristics and determine the control parameters that lead to different behavior of the system output, periodic, quasi-periodic and chaos. The time series, attractor, Fast Fourier Transformation and bifurcation diagram for different values have been described.