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.
ABSTRACT
This research included the preparation and characterization of new demulsifies from natural and synthetic polymers of chitosan and polyvinyl alcohol that are environmentally friendly and at the same time have high efficacy comparable to emulsifiers. imported foreign. The prepared compounds were examined using infrared spectroscopy and nuclear magnetic resonance spectroscopy, and all the spectral signals of the polymers were in good agreement with the chemical composition of the polymers. And the melting and decomposition that occur on polymers at high temperatures. The effect of the length and type of side chain in the compositions of polymers on the process of water separation of oil emulsions w
... Show MoreIn this effort, we define a new class of fractional analytic functions containing functional parameters in the open unit disk. By employing this class, we introduce two types of fractional operators, differential and integral. The fractional differential operator is considered to be in the sense of Ruscheweyh differential operator, while the fractional integral operator is in the sense of Noor integral. The boundedness and compactness in a complex Banach space are discussed. Other studies are illustrated in the sequel.
Precision is one of the main elements that control the quality of a geodetic network, which defines as the measure of the network efficiency in propagation of random errors. This research aims to solve ZOD and FOD problems for a geodetic network using Rosenbrock Method to optimize the geodetic networks by using MATLAB programming language, to find the optimal design of geodetic network with high precision. ZOD problem was applied to a case study network consists of 19 points and 58 designed distances with a priori deviation equal to 5mm, to determine the best points in the network to consider as control points. The results showed that P55 and P73 having the minimum ellipse of error and considered as control points. FOD problem was applie
... Show MoreThe present work represents a theoretical study for the correction of spherical aberration of an immersion lens of axial symmetry operating under the effect of space charge, represented by a second order function and preassigned magnification conditions in a focusing of high current ion beams. The space charge depends strongly on the value of the ionic beam current which is found to be very effective and represents an important factor effecting the value of spherical aberration .The distribution of the space charge was measured from knowing it's density .It is effect on the trajectory of the ion beam was studied. To obtain the trajectories of the charged particles which satisfy the preassined potential the axial electrostatic potential w
... Show MoreThe problems of modeling the signal and dispersion properties of a second order recursive section in the integer parameter space are considered. The formulation and solution of the section synthesis problem by selective and dispersive criteria using the methods of integer nonlinear mathematical programming are given. The availability of obtaining both positive and negative frequency dispersion of a signal in a recursive section, as well as the possibility of minimizing dispersion distortions in the system, is shown.
The aim of this paper is to introduce the concepts of asymptotically p-contractive and asymptotically severe accretive mappings. Also, we give an iterative methods (two step-three step) for finite family of asymptotically p-contractive and asymptotically severe accretive mappings to solve types of equations.