The researcher [1-10] proposed a method for computing the numerical solution to quasi-linear parabolic p.d.e.s using a Chebyshev method. The purpose of this paper is to extend the method to problems with mixed boundary conditions. An error analysis for the linear problem is given and a global element Chebyshev method is described. A comparison of various chebyshev methods is made by applying them to two-point eigenproblems. It is shown by analysis and numerical examples that the approach used to derive the generalized Chebyshev method is comparable, in terms of the accuracy obtained, with existing Chebyshev methods.

Average per capita GDP income is an important economic indicator. Economists use this term to determine the amount of progress or decline in the country's economy. It is also used to determine the order of countries and compare them with each other. Average per capita GDP income was first studied using the Time Series (Box Jenkins method), and the second is linear and non-linear regression; these methods are the most important and most commonly used statistical methods for forecasting because they are flexible and accurate in practice. The comparison is made to determine the best method between the two methods mentioned above using specific statistical criteria. The research found that the best approach is to build a model for predi

The dispersion relation of linear quantum ion acoustic waves is derivate according to a fluid approach that depends on the kinetic description of the systems of charged particles model. We discussed the dispersion relation by changing its parameters and graphically represented. We found through graphs that there is full agreement with previous studies on the subject of interest. That motivates us to discuss the dispersion relation of waves depending on the original basic parameters that implicitly involved in the relationship which change the relationship by one way or another, such as electron Fermi temperature and the density at equilibrium state.

    In the presence of multi-collinearity problem, the parameter estimation method based on the ordinary least squares procedure is unsatisfactory. In 1970, Hoerl and Kennard insert analternative method labeled as estimator of ridge regression.

In such estimator, ridge parameter plays an important role in estimation. Various methods were proposed by many statisticians to select the biasing constant (ridge parameter). Another popular method that is used to deal with the multi-collinearity problem is the principal component method. In this paper,we employ the simulation technique to compare the performance of principal component estimator with some types of ordinary ridge regression estimators based on the value of t

In this research, the one of the most important model and widely used in many and applications is linear mixed model, which widely used to analysis the longitudinal data that characterized by the repeated measures form .where estimating linear mixed model by using two methods (parametric and nonparametric) and used to estimate the conditional mean and marginal mean in linear mixed model ,A comparison between number of models is made to get the best model that will represent the mean wind speed in Iraq.The application is concerned with 8 meteorological stations in Iraq that we selected randomly and   then we take a monthly data about wind speed over ten years Then average it over each month in corresponding year, so we g

    New class A^* (a,c,k,β,α,γ,μ)  is introduced of meromorphic univalent functions with positive coefficient f(z)=â–¡(1/z)+∑_(n=1)^∞▒〖a_n z^n 〗,(a_n≥0,z∈U^*,∀ n∈ N={1,2,3,…}) defined by the integral operator in the punctured unit disc U^*={z∈C∶0<|z|<1}, satisfying |(z^2 (I^k (L^* (a,c)f(z)))^''+2z(I^k (L^* (a,c)f(z)))^')/(βz(I^k (L^* (a,c)f(z)))^''-α(1+γ)z(I^k (L^* (a,c)f(z)))^' )|<μ,(0<μ≤1,0≤α,γ<1,0<β≤1/2 ,k=1,2,3,… ) . Several properties were studied like coefficient estimates, convex set and weighted mean.