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.
Volterra – Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained
... Show MoreThis manuscript presents several applications for solving special kinds of ordinary and partial differential equations using iteration methods such as Adomian decomposition method (ADM), Variation iterative method (VIM) and Taylor series method. These methods can be applied as well as to solve nonperturbed problems and 3rd order parabolic PDEs with variable coefficient. Moreover, we compare the results using ADM, VIM and Taylor series method. These methods are a commination of the two initial conditions.
Air pollution from various sources is one of the most serious environmental problems, especially after pollutants are deposited on the surface of the soil and leaves of the plants and then transferred to the rest of the plant and entering food chains. The present study was conducted to determine the effects of air pollution on different biochemical parameters in Eucalyptus sp. and calculation the Air Pollution Tolerance Index. The selected plant leaves were collected from five sites, four of them within the city of Baghdad, namely Al-Jadriya, Al-Andlous, Al-Doura and close to the private generators to represent the urban areas and Abu Ghraib site to represent the rural area. The leaves were taken on a seasonal basis for the period from Octo
... Show MoreThe building of Basrah University located in a rural area at Gramat Ali, its consist of seven colleges and very high number of students, lecturers ,and employers. Therefore, the intersections which leading to university building suffer congestion at morning peak hour (8-9) A.M and evening peak hour (2-3) P.M. In this study we collected the data in intersections which leading to university building at peak hour at same time, then we had analysis this data by using the highway capacity manual (HCM) and program (HCS). Also, we collected that data in University entries with classification of vehicles according to types and number of passengers at peak hour. Then we studied the number of proposals to riddance the congestion, such as the effe
... Show MoreThe buildup factor of cylindrical samples (shields) for Brass, Copper & lead (Brass, Cu, Pb (was studied, where buildup factor were calculated with thickness between (0-12) m.f.p. for Co60 and Cs137sources with activities (30) & (41) MBq respectively , using scintillation detector NaI(T?) with (3"×3")volume .The results shows increases of buildup factor for low atomic number(Z) samples where the energy of radiation source was constant, also shows increases of buildup factor with decreases the energy of radiation source. An empirical equation was obtained using Matlab7 program this equation have agreements with most obtained data for 96%.
This paper investigated in the numerical simulation model to calculate the Earth magnetic field components at north provinces of Najaf city (Longitude 44.316 o -44.3592o E and Latitude 32.0508o - 32.0256o N). The components of the Earth magnetic field (total intensity (F), horizontal intensity (H), declination (D), inclination (I), the north component(X), the east component(Y), and Down component(Z)) were found by using spherical harmonic world magnetic model (WMM2010). A great deal of anomaly has been discovered in all components of the Earth magnetic field at the selected region (Long. 44.345o-44.335o E, Lat.32.042o-32.032o N) using Kriging method.
... Show MoreKE Sharquie, AA Noaimi, ZT Burhan, Journal of Cosmetics, Dermatological Sciences and Applications, 2016 - Cited by 9
the Objective of study is to measure the quality of medical service level, in the Iraq public hospitals ,presented by special words ,private hospitals, and compare between them, by knowing the level of recipients satisfaction of medical service for all dimensions of quality service, and then measuring satisfaction with the quality of medical service as a whole for both of them, which have been prepared in questionnaire form, included two main directions, first to determine the level of satisfaction when, recipients of medical service is not dimensions quality of service in accordance with the Scale Servqual by (Parasurman et .al 1988), consisting of five di
... Show MoreOriginal Research Paper Mathematics 1-Introduction : In the light of the progress and rapid development of the applications of research in applications fields, the need to rely on scientific tools and cleaner for data processing has become a prominent role in the resolution of decisions in industrial and service institutions according to the real need of these methods to make them scientific methods to solve the problem Making decisions for the purpose of making the departments succeed in performing their planning and executive tasks. Therefore, we found it necessary to know the transport model in general and to use statistical methods to reach the optimal solution with the lowest possible costs in particular. And you know The Transportatio
... Show MorePraise be to God alone, and prayers and peace be upon the one after whom there is no prophet, and after:
This is a regular judicial search for the issuance, validity, and cancellation of regulations in the Saudi system. It came in an introduction and four demands and a conclusion of the most important results, then a list of the most important sources and references, in which I presented: A brief study on the issuance of regulations in the Kingdom of Saudi Arabia and the stages that they pass through, their validity and application, and the rules that govern this system in terms of people, places and times, then canceling and amending regulations And its rulings, I referred to it to the original sources approved in this section,
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