Dec 01, 2023Open Access
The traditional numerical computation of the first and higher derivatives of a given function f(x) of a single argument x by central differencing is known to involve aspects of both accuracy and precision. However, central difference formulas are useful only for interior points not for a certain number of end points belonging to a given grid of points. In order to get approximations of a desired derivative at all points, one has to use asymmetric difference formulas at points where central diffe...
Aug 15, 2023Open Access
This article considered the development of a two-point hybrid method for the numerical solution of initial value problems of second order ordinary differential Equations (ODEs) using power series and exponentially-fitted basis function. Interpolation and collocation techniques were used to derive the method. The method was implemented in predictor-corrector mode. In order to increase the accuracy of the results of the method, the predictor was designed to have same order of accuracy as the corre...
Apr 24, 2022Open Access
This study is aimed to investigate the acceleration response of the non-commutated Direct Current (DC) linear actuator in a numerical approach. The linear actuator is often driven with the specified wave digital signal processing (DSP), which gets forced vibration. The acceleration response of the actuator matters because it is related to vibration intensity. As well, the experiments and technical datasheets report that after the resonance frequency, the acceleration decreased, and the vibration...
Aug 19, 2021Open Access
At least a minority of planets, moons and other bodies exist within significant external astrophysical fields. The ambient field problem is more relevant to these bodies than the classical dynamo problem, but remains relatively little studied. This paper will concern with the effect of axisymmetric and non-axi- symmetric ambient field on a spherical, axisymmetric dynamo model, through nonlinear calculations with α-quenching feedback. Ambient fields of varying strengths are imposed in the model. ...
May 20, 2021Open Access
In this paper, we establish some mid-point type and trapezoid type inequalities via a new class of fractional integral operators which is introduced by Ahmad et al. We derive a new fractional-type integral identity to obtain Dragomir-Agarwal inequality for m-convex mappings. Moreover, some inequalities of Hermite-Hadamard type for m-convex mappings are given related to fractional integrals with exponential kernels. The results presented provide extensions of those given in earlier works.
Feb 26, 2021Open Access
In this paper, we present formulas that turn finite power series into series of shifted Chebyshev polynomials of the first kind. Thereafter, we derive formulas for coefficients of economized power series obtained by truncating the resulting Chebyshev series. To illustrate the utility of our formulas, we apply them to the solution of first order ordinary differential equations via Taylor methods and to solving the Schrödinger equation (SE) for a spherically symmetric hyperbolic potential via...
Sep 29, 2020Open Access
In this paper, we have established a new identity related to Katugampola fractional integrals which generalize the results given by Topul et al. and Sarikaya and Budak. To obtain our main results, we assume that the absolute value of the derivative of the considered function is p-convex. We derive several parameterized generalized Hermite-Hadamard inequalities by using the obtained equation. More new inequalities can be presented by taking special parameter values for , and p. Also, we provide...
Aug 28, 2020Open Access
Vedic mathematics is found to be very effective and sound for mental calculations in mathematics. Sutras and sub sutras have beautiful and striking tricks for fast and easy for mathematical calculations. In this article, we explore on importance of Vedic Mathematics with thematic analysis. Vedic Math provides more systematic, simplified, unified and faster than the conventional system. A significant and interesting invention which has led to various applications in all the disciplines is the dev...
Aug 18, 2020Open Access
In this section the Successive approximate method (S.A.M) introduced for solving the Wu-Zhang systems, a (1 1)-dimensional nonlinear dispersive wave equation, this method shows us that the technique provided without disorder, in this model of convergence power series with a simple calculated ingredients and gives effective results.
Jul 23, 2020Open Access
This paper presents economized power series for the Gaussian function. The economization is accomplished by utilizing the “usual” and the “shifted” Chebyshev polynomials of the first kind. The resulting economized series are applied to the solution of the radial Schrödinger equation with the attractive Gaussian potential via the asymptotic iteration method (AIM). The obtained bound state energies are compared with those given by the same method when the Taylor expansion is used to approxima...