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.
Receipt date:06/23/2020 accepted date:7/15/2020 Publication date:12/31/2021
This work is licensed under a Creative Commons Attribution 4.0 International License
The executive authority differs from one country to another, as it differs from a federal state to another according to the nature of the applied political systems, so this research focused on federal states according to their political systems, then going into the details of the executive authority and its role In the federal states by referring to the four federal experiments
... Show MoreTest method was developed radioimmunotherapy to appoint in two groups of patients infected with a uterine tumor Great conditions in tumor tissue benign and malignant Ddh teacher radioactive iodine isotope
This study aimed to identify the alterations of liver in the quail (Coturnix coturnix) exposed by nanosilver particles.45 quail (females) were collected from agriculture research center in Abu-Ghraib, divided into (6) groups including: T1(12 quails were exposed to 4ppm), T2 (12 quails were exposed to 8ppm) and T3 (12 quails were exposed to 12ppm) of silver nanoparticles solution for 60 days. As well as three groups for control (3 females for each). Birds were dissected to isolate livers for histological preperations after fixation with Bouin's fluid, Routine stains Hematoxyline and eosin were used. Histological study showed that the structure of liver in a control groups consist of hepatocytes arranged radially cords around the central vein
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