In this paper we use Bernstein polynomials for deriving the modified Simpson's 3/8 , and the composite modified Simpson's 3/8 to solve one dimensional linear Volterra integral equations of the second kind , and we find that the solution computed by this procedure is very close to exact solution.

In this article, we design an optimal neural network based on new LM training algorithm. The traditional algorithm of LM required high memory, storage and computational overhead because of it required the updated of Hessian approximations in each iteration. The suggested design implemented to converts the original problem into a minimization problem using feed forward type to solve non-linear 3D - PDEs. Also, optimal design is obtained by computing the parameters of learning with highly precise. Examples are provided to portray the efficiency and applicability of this technique. Comparisons with other designs are also conducted to demonstrate the accuracy of the proposed design.

This study presents a practical method for solving fractional order delay variational problems. The fractional derivative is given in the Caputo sense. The suggested approach is based on the Laplace transform and the shifted Legendre polynomials by approximating the candidate function by the shifted Legendre series with unknown coefficients yet to be determined. The proposed method converts the fractional order delay variational problem into a set of (n ＋ 1) algebraic equations, where the solution to the resultant equation provides us the unknown coefficients of the terminated series that have been utilized to approximate the solution to the considered variational problem. Illustrative examples are given to show that the recommended appro

A mathematical model and associated computer program were developed to simulate the steady state operation of wiped film evaporators for the concentration of glycerol-water solution. In this model, various assumptions were made to facilitate the mathematical model of the wiped film evaporator. The fundamental phenomena described were: sensible heating of the solution and vaporization of water. Physical property data were coded into the computer program, which performs the calculations of this model. Randomly selected experiments were carried out in a small scale wiped film evaporator from ALVAL COMPANY, using different concentrations of the glycerol solution (10, 30 and 50 Wt. %) for different feed rates (30, 50, 80, 100 and 120 l/h) and

We propose a new object tracking model for two degrees of freedom mechanism. Our model uses a reverse projection from a camera plane to a world plane. Here, the model takes advantage of optic flow technique by re-projecting the flow vectors from the image space into world space. A pan-tilt (PT) mounting system is used to verify the performance of our model and maintain the tracked object within a region of interest (ROI). This system contains two servo motors to enable a webcam rotating along PT axes. The PT rotation angles are estimated based on a rigid transformation of the the optic flow vectors in which an idealized translation matrix followed by two rotational matrices around PT axes are used. Our model was tested and evaluated

this paper presents a novel method for solving nonlinear optimal conrol problems of regular type via its equivalent two points boundary value problems using the non-classical