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.
The changes of the tectonic boundary locations between the stable and unstable shelf on different version of the tectonic maps of Iraq is discussed. It is found that the location of the boundary varies due to philosophy and the type of the geological parameters. It is used the stratigraphic, geophysical, structural, geochemical, hydrological and others information in delineating the boundary. The deep crustal structures obtained by using gravity data show that the boundary shifted toward the west by about 100 km in southern Iraq. According to the review, and when taking in consideration all the geological and geophysical parameters from the lower crust to the earth surface, it is believed that the boundary is not a line but it is a tecto
... Show MoreIn this paper, the necessary optimality conditions are studied and derived for a new class of the sum of two Caputo–Katugampola fractional derivatives of orders (α, ρ) and( β,ρ) with fixed the final boundary conditions. In the second study, the approximation of the left Caputo-Katugampola fractional derivative was obtained by using the shifted Chebyshev polynomials. We also use the Clenshaw and Curtis formula to approximate the integral from -1 to 1. Further, we find the critical points using the Rayleigh–Ritz method. The obtained approximation of the left fractional Caputo-Katugampola derivatives was added to the algorithm applied to the illustrative example so that we obtained the approximate results for the stat
... Show MoreMolecular barcoding was widely recognized as a powerful tool for the identification of organisms during the past decade; the aim of this study is to use the molecular approach to identify the diatoms by using the environmental DNA. The diatom specimens were taken from Tigris River. The environmental DNA(e DNA) extraction and analysis of sequences using the Next Generation Sequencing (NGS) method showed the highest percentage of epipelic diatom genera including Achnanthidium minutissimum (Kützing) Czarnecki, 1994 (21.1%), Cocconeis placentula Ehrenberg, 1838 (21.3%) and Nitzschia palea (Kützing) W. Smith, 1856 (16.3%).
Five species of diatoms: Achnanthidiu
... Show MoreThe research involved attempt to inhibit the corrosion of Al-Si-Cu alloy in 2.5x10-3 mol.dm-3 NaOH solution (pH=11.4) by addition of six different inhibitors with three concentrations (1x10-3, 1x10-2, and 0.1 mol.dm-3). These inhibitors include three organic materials (sodium acetate, sodium benzoate, and sodium oxalate) and three inorganic materials (sodium chromate, disodium phosphate, and sodium sulphate). The data that concerning polarization behaviour are calculates which include the corrosion potential (Ecorr) and current density (icorr), cathodic and anodic Tafel slopes (bc & ba), and polarization resistance (Rp). Protection efficiency (P%) and activation energy (Ea) values were calculated for inhibition by the six inhibitors. The
... Show MoreIn this paper, we present a Branch and Bound (B&B) algorithm of scheduling (n) jobs on a single machine to minimize the sum total completion time, total tardiness, total earliness, number of tardy jobs and total late work with unequal release dates. We proposed six heuristic methods for account upper bound. Also to obtain lower bound (LB) to this problem we modified a (LB) select from literature, with (Moore algorithm and Lawler's algorithm). And some dominance rules were suggested. Also, two special cases were derived. Computational experience showed the proposed (B&B) algorithm was effective in solving problems with up to (16) jobs, also the upper bounds and the lower bound were effective in restr
... Show MoreIn this research, the nonparametric technique has been presented to estimate the time-varying coefficients functions for the longitudinal balanced data that characterized by observations obtained through (n) from the independent subjects, each one of them is measured repeatedly by group of specific time points (m). Although the measurements are independent among the different subjects; they are mostly connected within each subject and the applied techniques is the Local Linear kernel LLPK technique. To avoid the problems of dimensionality, and thick computation, the two-steps method has been used to estimate the coefficients functions by using the two former technique. Since, the two-
... Show MoreThe objective of the research is to identify the effect of the five-finger strategy on the holistic thinking of chemistry students in the second intermediate grade, where the sample consisted of 60 female students in a second classfrom one of the intermediate schools in Baghdad city, divided into two groups: control and experimental. The experimental design was based on the partial control; the scientific course was defined in the third and fourth chapters of the science book of the second intermediate grade.The two research tools were prepared: the attainment test with the scientific course and the holistic thinking scale paragraph (36) of multiple-choice pre- and posttest. The results showed a statistically significant difference between
... Show MoreBackground: Congenital club foot is a complex deformity of foot .It is a collection of different abnormalities, with different etiologies. Consequently, Severity varies with difficulties in evaluating treatment strategies with outcome results. The treatment of congenital club foot remains controversial. Usually, the orthopedist's goal is to obtain anatomically and functionally normal feet in all patients. Objective: To asses short term follow up result of conservatively treated club feet in relation to the age
... Show Morein this paper fourth order kutta method has been used to find the numerical solution for different types of first liner