This research studying the phenomenon of Doppler (frequency Doppler) as a method through which the direction and speed of the blood cells flows in blood vessels wear measured. This Doppler frequency is relied upon in medicine for measuring the speed of blood flow, because the blood flow is an important concept from the concepts of medicine. It represents the function and efficient of the heart and blood vessels in the body so any defect in this function will appear as a change in the speed of blood flow from the normal value assumed. As this speed changes alot in cases of  disease and morbidity  of the heart, so in order to identify the effect of changing the Doppler frequency on the speed of blood flow and the relationship of

In this paper we will investigate some Heuristic methods to solve travelling salesman problem. The discussed methods are Minimizing Distance Method (MDM), Branch and Bound Method (BABM), Tree Type Heuristic Method (TTHM) and Greedy Method (GRM).

The weak points of MDM are manipulated in this paper. The Improved MDM (IMDM) gives better results than classical MDM, and other discussed methods, while the GRM gives best time for 5≤ n ≤500, where n is the number of visited cities.

In this article, the numerical and approximate solutions for the nonlinear differential equation systems, represented by the epidemic SIR model, are determined. The effective iterative methods, namely the Daftardar-Jafari method (DJM), Temimi-Ansari method (TAM), and the Banach contraction method (BCM), are used to obtain the approximate solutions. The results showed many advantages over other iterative methods, such as Adomian decomposition method (ADM) and the variation iteration method (VIM) which were applied to the non-linear terms of the Adomian polynomial and the Lagrange multiplier, respectively. Furthermore, numerical solutions were obtained by using the fourth-orde Runge-Kutta (RK4), where the maximum remaining errors showed th

This paper deals with testing a numerical solution for the discrete classical optimal control problem governed by a linear hyperbolic boundary value problem with variable coefficients. When the discrete classical control is fixed, the proof of the existence and uniqueness theorem for the discrete solution of the discrete weak form is achieved. The existence theorem for the discrete classical optimal control and the necessary conditions for optimality of the problem are proved under suitable assumptions. The discrete classical optimal control problem (DCOCP) is solved by using the mixed Galerkin finite element method to find the solution of the discrete weak form (discrete state). Also, it is used to find the solution for the discrete adj

This article deals with the approximate algorithm for two dimensional multi-space fractional bioheat equations (M-SFBHE). The application of the collection method will be expanding for presenting a numerical technique for solving M-SFBHE based on “shifted Jacobi-Gauss-Labatto polynomials” (SJ-GL-Ps) in the matrix form. The Caputo formula has been utilized to approximate the fractional derivative and to demonstrate its usefulness and accuracy, the proposed methodology was applied in two examples. The numerical results revealed that the used approach is very effective and gives high accuracy and good convergence.

  We study one example of hyperbolic problems it's Initial-boundary string problem with two ends. In fact we look for the solution in weak sense in some sobolev spaces. Also we use energy technic with Galerkin's method to study some properties for our problem as existence and uniqueness

This paper focuses on the most important element of scientific research: the research problem which is confined to the concept of concern or concern surrounding the researcher about any event or phenomenon or issue paper and need to be studied and addressed in order to find solutions for them, to influence the most scientific research steps from asking questions and formulating hypotheses, to employ suitable methods and tools to choose the research and sample community, to employ measurement and analysis tools. This problem calls for a great effort by the researcher intellectually or materially to develop solutions.

The Assignment model is a mathematical model that aims to express a real problem facing factories and companies which is characterized by the guarantee of its activity in order to make the appropriate decision to get the best allocation of machines or jobs or workers on machines in order to increase efficiency or profits to the highest possible level or reduce costs or time To the extent possible, and in this research has been using the method of labeling to solve the problem of the fuzzy assignment of real data has been approved by the tire factory Diwaniya, where the data included two factors are the factors of efficiency and cost, and was solved manually by a number of iterations until reaching the optimization solution,

Transportation problems are considered as a type of operation research problems. In fact, they deal with scheduling transportation of goods from their source to delivery sites in the minimum cost.

Such problems can be solved by the available traditional methods, which include; North-West corner, Least cost and Vogel’s method. As well as if this transportation problem is considered as a linear program it can also be solved by using Simplex method

The goal of the present study is to compare different research methods to provide the optimal and minimum cost.

This study was applied to resolve a transportation problem related to land Transportation Company, w