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.

   In this paper, we applied the concept of the error analysis using the linearization method and new condition numbers constituting optimal bounds in appraisals of the possible errors. Evaluations of finite continued fractions, computations of determinates of tridiagonal systems, of determinates of second order and a "fast" complex multiplication. As in Horner's scheme, present rounding error analysis of product and summation algorithms. The error estimates are tested by numerical examples. The executed program for calculation is "MATLAB 7" from the website "Mathworks.com

In this article, the backstepping control scheme is proposed to stabilize the fractional order Riccati matrix differential equation with retarded arguments in which the fractional derivative is presented using Caputo's definition of fractional derivative. The results are established using Mittag-Leffler stability. The fractional Lyapunov function is defined at each stage and the negativity of an overall fractional Lyapunov function is ensured by the proper selection of the control law. Numerical simulation has been used to demonstrate the effectiveness of the proposed control scheme for stabilizing such type of Riccati matrix differential equations.

      This paper examines the finding of spacewise dependent heat source function in pseudoparabolic equation with initial and homogeneous Dirichlet boundary conditions, as well as the final time value / integral specification as additional conditions that ensure the uniqueness solvability of the inverse problem. However, the problem remains ill-posed because tiny perturbations in input data cause huge errors in outputs. Thus, we employ Tikhonov’s regularization method to restore this instability. In order to choose the best regularization parameter, we employ L-curve method. On the other hand, the direct (forward) problem is solved by a finite difference scheme while the inverse one is reformulated as an optimization problem. The

In this research, the covariance estimates were used to estimate the population mean in the stratified random sampling and combined regression estimates. were compared by employing the robust variance-covariance matrices estimates with combined regression estimates by employing the traditional variance-covariance matrices estimates when estimating the regression parameter, through the two efficiency criteria (RE) and mean squared error (MSE). We found that robust estimates significantly improved the quality of combined regression estimates by reducing the effect of outliers using robust covariance and covariance matrices estimates (MCD, MVE) when estimating the regression parameter. In addition, the results of the simulation study proved

     In this study, an efficient novel technique is presented to obtain a more accurate analytical solution to nonlinear pantograph differential equations. This technique combines the Adomian decomposition method (ADM) with the homotopy analysis method concepts (HAM). The whole integral part of HAM is used instead of an integral part of ADM approach to get higher accurate results. The main advantage of this technique is that it  gives a large and more extended convergent region of iterative approximate solutions for long time intervals that rapidly converge to the exact solution. Another advantage is capable of providing a continuous representation of the approximate solutions, which gives  better information over whole time interv

The study investigated the behaviour of asphalt concrete mixes for aggregate gradations, according to the Iraqi specification using the Bailey method designed by an Excel spreadsheet. In mixing aggregates with varying gradations (coarse and fine aggregate), The Bailey method is a systematic methodology that offers aggregate interlocking as the backbone of the framework and a controlled gradation to complete the blends. Six types of gradation are used according to the bailey method considered in this study. Two-course prepared Asphalt Concrete Wearing and Asphalt Concrete binder, the Nominal Maximum Aggregate Sizes (NMAS) of the mixtures are 19 and 12.5 mm, respectively. The total number of specimens was 240 for both layers (15 samp

A newly developed analytical method characterized by its speed and sensitivity for the determination of metformin-HCl via the formation of complex for metformin-HCl-OH--copper(II) ion from the gel bead system by continuous flow injection analysis. The method is based on the imbedded copper(II) ion in the gel bead structure can be used in the reaction for the formation of red –magneta colour complex(λmax. =530nm) formed by direct reaction of the drug with the released copper (II) ion from the gel bead in alkaline medium. Linear dynamic range for the absorbance versus metformin concentration was 0.001-1 mmol.L-1 while C.O.D was (r2% =95.33%) . The L.O.Q was 0.868mmol.L-1.L.O.D (S/N=3)=0.5μmol.L-1 from the step wise dilution for the min

Films of PMMA and copper sulphate doped PMMA have been prepared by casting method. Absorbance and transmittance spectra were recorded in the wavelength range (300-900) nm in order to calculate, single oscillator energy, dispersion energy, average oscillator strength, the refractive index at infinite wavelength, M-1 and M -3 moments of the optical spectra, it was found that all these parameters were effected by doping.

Feature extraction provide a quick process for extracting object from remote sensing data (images) saving time to urban planner or GIS user from digitizing hundreds of time by hand. In the present work manual, rule based, and classification methods have been applied. And using an object- based approach to classify imagery. From the result, we obtained that each method is suitable for extraction depending on the properties of the object, for example, manual method is convenient for object, which is clear, and have sufficient area, also choosing scale and merge level have significant effect on the classification process and the accuracy of object extraction. Also from the results the rule-based method is more suitable method for extracting