Background This study establishes a mathematically consistent and computational framework for the simultaneous identification of two time-dependent coefficients in a one-dimensional second-order parabolic partial differential equation. The considered problem is governed by nonlocal initial, boundary, and integral overdetermination conditions. Methods The direct problem is solved using the Crank-Nicolson finite difference method (FDM), which ensures unconditional stability and second-order accuracy in both spatial and temporal discretizations. The corresponding inverse problem is reformulated as a nonlinear regularized least-squares optimization problem and efficiently solved used the MATLAB subroutine
Background: Early detection of subclinical left ventricular (LV) systolic dysfunction is crucial and could influence patients' prognosis by aiding the clinician to candidate patients for better management.
Objective: To detect early LV systolic dysfunction in asymptomatic patient with chronic aortic regurgitation by two dimensional speckle tracking echocardiography.
Methods: Sixty one asymptomatic patients with chronic aortic regurgitation, with no ischemic heart diseases (by coronary angiography) or conductive heart diseases, no diabetes mellitus, no hypertension, and no other valvular heart diseases (group 1) and fifty age and sex-matched healthy subjects (
... Show MoreIn this article, the solvability of some proposal types of the multi-fractional integro-partial differential system has been discussed in details by using the concept of abstract Cauchy problem and certain semigroup operators and some necessary and sufficient conditions.
This research sheds light on the use of metal in the manufacture of jewelry, which is represented by ornamental tools in the period between the third and second millennium BC, in addition to the most important molds used in their manufacture. Man has been interested in metals since early ages, and was able to make tools that he uses in his daily life, especially jewelry. And the Syrian people got acquainted with the types of minerals, their characteristics, and how to deal with them. Minerals played an effective and prominent role in the economy of ancient Syria. Trade with those countries and secure their roads.
The effective insulation design of the stress grading (SG) system in form-wound stator coils is essential for preventing partial discharges and excessive heat generation under pulse-width modulation excitation. This paper proposes a method to find the optimal insulation design of the SG system aimed at reducing the dielectric and thermal stresses in the machine coil. The non-uniform transmission line model is used to predict the voltage propagation along the overhang, SG, and slot regions considering the variation in the physical properties of the insulation layers. The machine coil parameters for different insulation materials are calculated by using the finite element method. Two optimization algorithms, fmincon and particle swarm optimiz
... Show MoreThe aim of this paper is to present a method for solving third order ordinary differential equations with two point boundary condition , we propose 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, many examples are presented to demonstrate the applicability, accuracy and efficiency of the method by compared with conventional method .
Orthogonal polynomials and their moments serve as pivotal elements across various fields. Discrete Krawtchouk polynomials (DKraPs) are considered a versatile family of orthogonal polynomials and are widely used in different fields such as probability theory, signal processing, digital communications, and image processing. Various recurrence algorithms have been proposed so far to address the challenge of numerical instability for large values of orders and signal sizes. The computation of DKraP coefficients was typically computed using sequential algorithms, which are computationally extensive for large order values and polynomial sizes. To this end, this paper introduces a computationally efficient solution that utilizes the parall
... Show MoreA modify approach for approximating an analytical solution of some PDEs with fractional order is the Variational Adomian decomposition methodology (VIADM). We provide several examples to support our conclusions. the results of the solutions process showed that the suggested approach is highly simple, dependable, and effective. The outcomes demonstrate the effectiveness and accuracy of current technology in solving a variety of applied scientific nonlinear challenges. All of the calculations and visualizations were done using the MATLAB R2024B software. In Caputo Sense, fractional derivatives are mentioned. Additionally, a graphical representation of the solutions to a few cases was created. Solution graphs are displayed for problems
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