This paper is concerned with finding solutions to free-boundary inverse coefficient problems. Mathematically, we handle a one-dimensional non-homogeneous heat equation subject to initial and boundary conditions as well as non-localized integral observations of zeroth and first-order heat momentum. The direct problem is solved for the temperature distribution and the non-localized integral measurements using the Crank–Nicolson finite difference method. The inverse problem is solved by simultaneously finding the temperature distribution, the time-dependent free-boundary function indicating the location of the moving interface, and the time-wise thermal diffusivity or advection velocities. We reformulate the inverse problem as a non-linear optimization problem and use the lsqnonlin non-linear least-square solver from the MATLAB optimization toolbox. Through examples and discussions, we determine the optimal values of the regulation parameters to ensure accurate, convergent, and stable reconstructions. The direct problem is well-posed, and the Crank–Nicolson method provides accurate solutions with relative errors below 0.006% when the discretization elements are M=N=80. The accuracy of the forward solutions helps to obtain sensible solutions for the inverse problem. Although the inverse problem is ill-posed, we determine the optimal regularization parameter values to obtain satisfactory solutions. We also investigate the existence of inverse solutions to the considered problems and verify their uniqueness based on established definitions and theorems.
Transportation and distribution are the most important elements in the work system for any company, which are of great importance in the success of the chain work. Al-Rabee factory is one of the largest ice cream factories in Iraq and it is considered one of the most productive and diversified factories with products where its products cover most areas of the capital Baghdad, however, it lacks a distribution system based on scientific and mathematical methods to work in the transportation and distribution processes, moreover, these processes need a set of important data that cannot in any way be separated from the reality of fuzziness industrial environment in Iraq, which led to use the fuzzy sets theory to reduce the levels of uncertainty.
... Show MoreTime affects all elements of the intellectual scene or the theatrical scene. It came along with the theatrical doctrines according to the conditions of those doctrines and their conceptual ideas or the method of their mechanisms in the application. While it is classically or realistically integrated, we see it in the expressionist doctrine inconsistent and its inconsistency makes it responsive for the deconstruction strategy. Hence the researcher entitled his study (deconstruction the theatrical time in the expressionist doctrine) so that deconstruction would be a field for his study. The study starts with an introduction presenting the research problem, importance and objective. The theoretical framework consisted of three s
... Show MoreIn this study many specimen s were prepared from 2024-T3 Aluminum alloy for corrosion test by the dimensions of (15*15*3) mm according to ASTM G71-31 and then subjected to shot peening process at different time (15, 30, 45) minutes using steel ball having a diameter of 2.75 mm and Rockwell Hardness of 55RC to induce compressive residual stress which were measured using X-Ray diffraction method, surface roughness and hardness were tested before and after peening. Electrochemical corrosion test by Tafel extrapolation method was carried out in an environment of 3 .5% NaCl solutions (sea water) where Corrosion rate calculated using Tafle equation.
The obtained results show a favorable influence of SP treatment
... Show MoreTime is very important in educational institutions. It is also one of our contemporary problem ‚as time is a clear – cut and limited factor‚ it demands that administrators should monitor it by administering and monitoring the principles of time.
Hence‚ the researcher attempts to identify the skills of administrating time and the reasons that cause the waste of time of the Heads of Departments at university of Baghdad.
Significance of the research:
Time is very important to all educational administrators and one of them is the institutions of Higher education. One of the
... Show MoreIn this paper, the effective computational method (ECM) based on the standard monomial polynomial has been implemented to solve the nonlinear Jeffery-Hamel flow problem. Moreover, novel effective computational methods have been developed and suggested in this study by suitable base functions, namely Chebyshev, Bernstein, Legendre, and Hermite polynomials. The utilization of the base functions converts the nonlinear problem to a nonlinear algebraic system of equations, which is then resolved using the Mathematica®12 program. The development of effective computational methods (D-ECM) has been applied to solve the nonlinear Jeffery-Hamel flow problem, then a comparison between the methods has been shown. Furthermore, the maximum
... Show MoreThe aim of this book is to present a method for solving high order ordinary differential equations with two point boundary condition of the different kind, we propose semi-analytic technique using two-point osculatory interpolation to construct polynomial solution. The original problem is concerned using two-points osculatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] . Also, we discussion the existence and uniqueness of solutions and many examples are presented to demonstrate the applicability, accuracy and efficiency of the methods by compared with conventional method .i.e. VIDM , Septic B-Spline , , NIM , HPM, Haar wavelets on one hand and to confirm the order convergence on the other
... Show MoreIn this paper, an efficient image segmentation scheme is proposed of boundary based & geometric region features as an alternative way of utilizing statistical base only. The test results vary according to partitioning control parameters values and image details or characteristics, with preserving the segmented image edges.
This paper investigates an effective computational method (ECM) based on the standard polynomials used to solve some nonlinear initial and boundary value problems appeared in engineering and applied sciences. Moreover, the effective computational methods in this paper were improved by suitable orthogonal base functions, especially the Chebyshev, Bernoulli, and Laguerre polynomials, to obtain novel approximate solutions for some nonlinear problems. These base functions enable the nonlinear problem to be effectively converted into a nonlinear algebraic system of equations, which are then solved using Mathematica®12. The improved effective computational methods (I-ECMs) have been implemented to solve three applications involving
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