The basic goal of this research is to utilize an analytical method which is called the Modified Iterative Method in order to gain an approximate analytic solution to the Sine-Gordon equation. The suggested method is the amalgamation of the iterative method and a well-known technique, namely the Adomian decomposition method. A method minimizes the computational size, averts round-off errors, transformation and linearization, or takes some restrictive assumptions. Several examples are chosen to show the importance and effectiveness of the proposed method. In addition, a modified iterative method gives faster and easier solutions than other methods. These solutions are accurate and in agreement with the series

     In this study, the electron energy distribution function (EEDF), the electron swarm parameters , the effective ionization coefficients, and the critical field strength (dielectric strength) in binary He-H₂ gas mixture which is used as cryogenic for high-temperature superconducting power applications,  are evaluated using two-term solution  of the Boltzmann equation over the range of E/N ( the electric field to gas density) from 1 to 100 Td ( 1 Td=10^-17 Vcm²) at temperature 77 K and pressure 2MPa, taking into account elastic ( momentum transfer) and inelastic cross-sections. Using the electron energy distribution function (EEDF) electron swarm parameters (electron drift velocity, mean electron e

The inverse kinematic equation for a robot is very important to the control robot’s motion and position. The solving of this equation is complex for the rigid robot due to the dependency of this equation on the joint configuration and structure of robot link. In light robot arms, where the flexibility exists, the solving of this problem is more complicated than the rigid link robot because the deformation variables (elongation and bending) are present in the forward kinematic equation. The finding of an inverse kinematic equation needs to obtain the relation between the joint angles and both of the end-effector position and deformations variables. In this work, a neural network has been proposed to solve the problem of inverse kinemati

Trickle irrigation is a system for supplying filtered water and fertilizer directly into the soil and water and it is allowed to dissipate under low pressure in an exact predetermined pattern. An equation to estimate the wetted area of unsaturated soil with water uptake by roots is simulated numerically using the HYDRUS-2D/3D software. In this paper, two soil types, which were different in saturated hydraulic conductivity were used with two types of crops tomato and corn, different values of emitter discharge and initial volumetric soil moisture content were assumed. It was assumed that the water uptake by roots was presented as a continuous sink function and it was introduced into Richard's equation in the unsaturated z

This study aimed to extraction of essential oil from peppermint leaves by using hydro distillation methods. In the peppermint oil extraction with hydro distillation method is studied the effect of the extraction temperature to the yield of peppermint oil. Besides it also studied the kinetics during the extraction process. Then, 2^nd -order mechanism was adopted in the model of hydro distillation for estimation many parameters such as the initial extraction rate, capacity of extraction and the constant rat of extraction with various temperature. The same model was also used to estimate the activation energy. The results showed a spontaneous process, since the  Gibbs free energy had a value negative sign.

The integral transformations is a complicated function from a function space into a simple function in transformed space. Where the function being characterized easily and manipulated through integration in transformed function space. The two parametric form of SEE transformation and its basic characteristics have been demonstrated in this study. The transformed function of a few fundamental functions along with its time derivative rule is shown. It has been demonstrated how two parametric SEE transformations can be used to solve linear differential equations. This research provides a solution to population growth rate equation. One can contrast these outcomes with different Laplace type transformations

     In this paper, we conduct some qualitative analysis that involves the global asymptotic stability (GAS) of the Neutral Differential Equation (NDE) with variable delay, by using  Banach contraction mapping theorem, to give some necessary conditions to achieve the GAS of the zero solution.

This paper presents a new numerical method for the solution of ordinary differential equations (ODE). The linear second-order equations considered herein are solved using operational matrices of Wang-Ball Polynomials. By the improvement of the operational matrix, the singularity of the ODE is removed, hence ensuring that a solution is obtained. In order to show the employability of the method, several problems were considered. The results indicate that the method is suitable to obtain accurate solutions.

The equation of Kepler is used to solve different problems associated with celestial mechanics and the dynamics of the orbit. It is an exact explanation for the movement of any two bodies in space under the effect of gravity. This equation represents the body in space in terms of polar coordinates; thus, it can also specify the time required for the body to complete its period along the orbit around another body. This paper is a review for previously published papers related to solve Kepler’s equation and eccentric anomaly. It aims to collect and assess changed iterative initial values for eccentric anomaly for forty previous years. Those initial values are tested to select the finest one based on the number of iterations, as well as the

In this paper, the blow-up solutions for a parabolic problem, defined in a bounded domain, are studied. Namely, we consider the upper blow-up rate estimate for heat equation with a nonlinear Neumann boundary condition defined on a ball in Rn.