This paper is devoted to an inverse problem of determining discontinuous space-wise dependent heat source in a linear parabolic equation from the measurements at the final moment. In the existing literature, a considerably accurate solution to the inverse problems with an unknown space-wise dependent heat source is impossible without introducing any type of regularization method but here we have to determine the unknown discontinuous space-wise dependent heat source accurately using the Haar wavelet collocation method (HWCM) without applying the regularization technique. This HWCM is based on finite-difference and Haar wavelets approximation to the inverse problem. In contrast to other numerical techniques, in HWCM, we used Haar functions that create a well-conditioned system of algebraic equations. The proposed method is stable and convergent because the numerical solution converges to the exact solution without observing any difficulty. Finally, some numerical examples are presented to verify the validity of the HWCM for different cases of the source term.
Abstract
The aim of the current research is to prepare an integrated learning program based on mathematics standards for the next generation of the NYS and to investigate its impact on the development of the teaching performance of middle school mathematics teachers and the future thinking skills of their students. To achieve the objectives of the research, the researcher prepared a list of mathematics standards for the next generation, which were derived from a list of standards. He also prepared a list of the teaching competencies required for middle school mathematics teachers in light of the list of standards, as well as clarified the foundations of the training program and its objectives and the mathematical
... Show MoreStarting from the term (forbidden montage) initiated by the French critic (Andre Bazin) as a method of processing the movies that depend on (mise en scene) achieved by the action of the camera and its ability to photograph and employ the depth of the field, in addition to the possibility of free movement without interruption in the filming environment in order to avoid montage as much as possible (the montage that distorts focus and distracts attention and moves away from realism, which is the most important theoretical pillar of Bazin in photography). The pursuit was behind a cinema that depicts its topics in one integrated snapshot with all its details thus approximating reality without any interference of montage. Our study sta
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Perhaps the methods of mask that Arab poets resorted to in our time are due to the conditions of oppression and political and social repression that the Arab poet suffered from; So he strived to circumvent it, and it became a justification for hiding behind it. The research is available on a number of topics that lead to the definition of the mask technique and the beginning of its prevalence in Arabic literature after the Second World War, especially in recent decades by benefiting from historical stories, fairy tales and legends of all kinds. As well as defining the mask idiomatically and linguistically, and the beginning of its use in ancient religious rituals, and the special place it had in Greek plays. Poets
... Show MoreStroke is the second largest cause of death worldwide and one of the most common causes of disability. However, several approaches have been proposed to deal with stroke patient rehabilitation like robotic devices and virtual reality systems, researchers have found that the brain-computer interfaces (BCI) approaches can provide better results. In this study, the electroencephalography (EEG) dataset from post-stroke patients were investigated to identify the effects of the motor imagery (MI)-based BCI therapy by investigating sensorimotor areas using frequency and time-domain features and to select particular methods that help in enhancing the MI-based BCI systems for stroke patients using EEG signal processing. Therefore, to detect
... Show MoreExtemporization is the ability of the actor to reflect his internal being. It gives a sort of confidence and an ability to show the personal countenance of the role away from tension and rigidity. By extemporization, it is possible to deal with and criticize the real living life so it is an intellectual, emotional, sensual, and perceptive process connected with the psychological energy and the emotional memory and all this goes under the control of the director and his instigations and instructions depending on what the text involves of intellectual, social and psychological motivators so it primarily depends on talent, chance and discussion. The research involves four chapters; the first contains the problem
... Show MoreComputer models are used in the study of electrocardiography to provide insight into physiological phenomena that are difficult to measure in the lab or in a clinical environment.
The electrocardiogram is an important tool for the clinician in that it changes characteristically in a number of pathological conditions. Many illnesses can be detected by this measurement. By simulating the electrical activity of the heart one obtains a quantitative relationship between the electrocardiogram and different anomalies.
Because of the inhomogeneous fibrous structure of the heart and the irregular geometries of the body, finite element method is used for studying the electrical properties of the heart.
This work describes t
... Show MoreThe accuracy of the Moment Method for imposing no-slip boundary conditions in the lattice Boltzmann algorithm is investigated numerically using lid-driven cavity flow. Boundary conditions are imposed directly upon the hydrodynamic moments of the lattice Boltzmann equations, rather than the distribution functions, to ensure the constraints are satisfied precisely at grid points. Both single and multiple relaxation time models are applied. The results are in excellent agreement with data obtained from state-of-the-art numerical methods and are shown to converge with second order accuracy in grid spacing.