This paper presents an alternative method for developing effective embedded optimized Runge-Kutta (RK) algorithms to solve oscillatory problems numerically. The embedded scheme approach has algebraic orders of 5 and 4. By transforming second-order ordinary differential equations (ODEs) into their first-order counterpart, the suggested approach solves first-order ODEs. The amplification error, phase-lag, and first derivative of the phase-lag are all nil in the embedded pair. The alternative method’s absolute stability is demonstrated. The numerical tests are conducted to demonstrate the effectiveness of the developed approach in comparison to other RK approaches. The alternative approach outperforms the current RK methods.
this paper give a proof of known conditions for the existence of peridic conincidence points of continuius maps using lindemann theotem on transcendental numbers
The aim of this paper is adopted to give an approximate solution for advection dispersion equation of time fractional order derivative by using the Chebyshev wavelets-Galerkin Method . The Chebyshev wavelet and Galerkin method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are described based on the Caputo sense. Illustrative examples are included to demonstrate the validity and applicability of the proposed technique.
In this work, we are concerned with how to find an explicit approximate solution (AS) for the telegraph equation of space-fractional order (TESFO) using Sumudu transform method (STM). In this method, the space-fractional order derivatives are defined in the Caputo idea. The Sumudu method (SM) is established to be reliable and accurate. Three examples are discussed to check the applicability and the simplicity of this method. Finally, the Numerical results are tabulated and displayed graphically whenever possible to make comparisons between the AS and exact solution (ES).
The aim of this paper is to study the nonlinear delay second order eigenvalue problems which consists of delay ordinary differential equations, in fact one of the expansion methods that is called the least square method which will be developed to solve this kind of problems.
The aim of this work is to detect the best operating conditions that effect on the removal of Cu2+, Zn2+, and Ni2+ ions from aqueous solution using date pits in the batch adsorption experiments. The results have shown that the Al-zahdi Iraqi date pits demonstrated more efficient at certain values of operating conditions of adsorbent doses of 0.12 g/ml of aqueous solution, adsorption time 72 h, pH solution 5.5 ±0.2, shaking speed 300 rpm, and smallest adsorbent particle size needed for removal of metals. At the same time the particle size of date pits has a little effect on the adsorption at low initial concentration of heavy metals. The adsorption of metals increases with increas
... Show MoreNew chalcones of -{ - - - y - - hi di z e- -y he y - - e e- - e- - - substituted phenyl have been prepared from condensation of a new of 4-[5-(4`-tolyl)1,3,4-thiadiazole-2-yl] benzaldehyde (which is synthesized by the reaction of 2- amino-5- (4`-tolyl) -1,3,4-thiadiazole and benzaldehyde) with 3- or 4- substituted acetophenones in alkaline medium. The physical, CHNS analysis and spectral data of the synthesized compounds were determined. The biological activity evaluated of new compounds showed that many of these compounds possess antiba
... Show MoreThe title compound, [Ru(C12H7Br2N2)2(CO)2], possesses a distorted octahedral environment about the Ru atom, with two cyclometallated 4,40-dibromoazobenzene ligands and two mutually cis carbonyl ligands. The donor atoms are arranged such that the N atoms are respectively trans to a carbonyl ligand and an aryl C atom. Comment The title compound, (I), has been prepared as a minor product of the reaction of Ru3(CO)12 and 4,40-dibromoazobenzene in refluxing n-octane; the major product is the cluster complex Ru3(3-NC6H4Br)2(CO)9 (Willis et al., 2005). Two strong (CO) absorptions at 2039 and 1991 cm1 in the IR spectrum of (I) are consistent with the presence of two mutually cis carbonyl groups. The crystal structure was investigated to ascertai
... Show MoreOil flow lines are used to transport oil and its derivatives from a well over long distances, and because oil wells produce other potentially corrosive products, such as carbon dioxide and Hydrogen sulfide, it is necessary to take methods to protect the pipeline from corrosion. One of these methods is the use of corrosion inhibitors in this study. Prepare 5-acetyl-2-anilino-4-dimethylaminothiazole and test it as a corrosion inhibitor on a sample of the Rumaila flow line at a constant temperature 25°C in (3.5%) NaCl and (3.5%) KCl solution in the absence and presence of different concentrations of inhibitor (0 mM, 0.01 mM, 0.03 M, 0.05 mM). by using liner polarization (Tafel slope). The inhibiter exhibited the best performance at hi
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