ABSTRICT:

  This study is concerned with the estimation of constant  and time-varying parameters in non-linear ordinary differential equations, which do not have analytical solutions. The estimation is done in a multi-stage method where constant and time-varying parameters are estimated in a straight sequential way from several stages. In the first stage, the model of the differential equations is converted to a regression model that includes the state variables with their derivatives and then the estimation of the state variables and their derivatives in a penalized splines method and compensating the estimations in the regression model. In the second stage, the pseudo- least squares method was used to es

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.

A non-polynomial spline (NPS) is an approximation method that relies on the triangular and polynomial parts, so the method has infinite derivatives of the triangular part of the NPS to compensate for the loss of smoothness inherited by the polynomial. In this paper, we propose polynomial-free linear and quadratic spline types to solve fuzzy Volterra integral equations (FVIE) of the 2nd kind with the weakly singular kernel (FVIEWSK) and Abel's type kernel. The linear type algorithm gives four parameters to form a linear spline. In comparison, the quadratic type algorithm gives five parameters to create a quadratic spline, which is more of a credit for the exact solution. These algorithms process kernel singularities with a simple techniqu

     In this research, the eccentricity will be calculated as well as the best height of satellite orbit that can used to transfer from that orbit around the Earth to construct an interplanetary trajectory, for example Mars, when the transfer can be accomplished by a simple impulse, that means the transfer consists of an elliptical orbit from the inner orbit (at a perigee point) to the outer orbit (at apogee point). We will determine Keplerian equation to find the value of a mean anomaly(M) by Rung-Cutta method.

There are several types of satellites orbits around the Earth, but by this study, we find that the best stable orbit to the satellite that is used to inter its orbit around Mars is the Medium Earth Orbit (MEO) at a hei

Model birefringence was measured for elliptical-core fibers with low ellipticities, note the birefringence depends strongly on the frequency, especially when fiber is being operated near the higher mode cutoff where ν  for circular fiber of the single-mode type that correspond to the birefringence maximum. When ν  this also correspond to the birefringence maximum that can be introduced in an elliptical core fiber while still operating in the single-mode regime near the higher mode cutoff. Also the birefringence is proportional to the fiber core ellipticity when core ellipticity is much less than unity, but this birefringence deviates from the linear for the large core ellipticities.

The researcher studied transportation problem because it's great importance in the country's economy. This paper which ware studied several ways to find a solution closely to the optimization, has applied these methods to the practical reality by taking one oil derivatives which is benzene product, where the first purpose of this study is, how we can reduce the total costs of transportation for product of petrol from warehouses in the province of Baghdad, to some stations in the Karsh district and Rusafa in the same province. Secondly, how can we address the Domandes of each station by required quantity which is depending on absorptive capacity of the warehouses (quantities supply), And through r

The purpose of this research paper is to present the second-order homogeneous complex differential equation   , where   , which is defined on the certain complex domain depends on solution behavior. In order to demonstrate  the relationship between the solution of the second-order of the complex differential equation and its coefficient of function, by studying the solution in certain cases: a meromorphic function, a coefficient of function, and if the solution is considered to be a transformation with another complex solution. In addition, the solution has been provided as a power series with some  applications.

This article addresses a new numerical method to find a numerical solution of the linear delay differential equation of fractional order , the fractional derivatives described in the Caputo sense. The new approach is to approximating second and third derivatives. A backward finite difference method is used. Besides, the composite Trapezoidal rule is used in the Caputo definition to match the integral term. The accuracy and convergence of the prescribed technique are explained. The results  are shown through numerical examples.