A method for Approximated evaluation of linear functional differential equations is described. where a function approximation as a linear combination of a set of orthogonal basis functions which are chebyshev functions .The coefficients of the approximation are determined by (least square and Galerkin’s) methods. The property of chebyshev polynomials leads to good results , which are demonstrated with examples.
In this paper, the proposed phase fitted and amplification fitted of the Runge-Kutta-Fehlberg method were derived on the basis of existing method of 4(5) order to solve ordinary differential equations with oscillatory solutions. The recent method has null phase-lag and zero dissipation properties. The phase-lag or dispersion error is the angle between the real solution and the approximate solution. While the dissipation is the distance of the numerical solution from the basic periodic solution. Many of problems are tested over a long interval, and the numerical results have shown that the present method is more precise than the 4(5) Runge-Kutta-Fehlberg method.
This paper tackles in detail the functional shift of parts of speech, such as the shift of a verbal clause to an adjectival clause, along with the types of such a shift. The researcher identified the important features of participles, as well as the concept of participles, adjectives, and their types. Also, the most important changes that affect the participles during such shifts. Further, an exposition is made of the different producers through which a verbal clause is changed into an adjectival one in Russian.
This type of functional shift in parts of speech is seen as a process of deriving most of the new words in contemporary Russian. Russian is very rich in new words, whether by way of processe
... Show MoreMany athletes believe that it enhances the level of performance during training and competition, in addition to compensating for fluids during exercise when the levels of temperature and humidity in the atmosphere rise during the athlete's intensive training, as it increases the requirements for fluid compensation to avoid the risk of potential thermal disorders. If training continues for more than an hour causing fatigue, athletes are advised to drink carbohydrate drinks that quickly convert to glucose in the blood, while sodium should be included in the fluids consumed during exercise or matches that last more than (1-2 hours). The effect of drinking a drink containing 12% carbohydrates and electrolytes before each half of a simul
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