This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

Pharmaceutical-instigated pollution is a major concern, especially in relation to aquatic environments and drugs such as meropenem antibiotics. Adsorbents, such as multi-walled carbon nanotubes, offer potential as means of removing polluting meropenem antibiotics and other similar compounds from water. In order to evaluate the effectiveness of multi-walled carbon nanotubes in this capacity, various experimental parameters, including contact time, initial concentration, pH, temperature and the dose of adsorbent have been investigated. The Langmuir and the Freundlich isotherm models have been used. The data obtained using a modified Langmuir model have been consistent with the experimental ones; the best pH value has been obtained to have the

This 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.

Some nonlinear differential equations with fractional order are evaluated using a novel approach, the Sumudu and Adomian Decomposition Technique (STADM). To get the results of the given model, the Sumudu transformation and iterative technique are employed. The suggested method has an advantage over alternative strategies in that it does not require additional resources or calculations. This approach works well, is easy to use, and yields good results. Besides, the solution graphs are plotted using MATLAB software. Also, the true solution of the fractional Newell-Whitehead equation is shown together with the approximate solutions of STADM. The results showed our approach is a great, reliable, and easy method to deal with specific problems in

An efficient combination of Adomian Decomposition iterative technique coupled with Laplace transformation to solve non-linear Random Integro differential equation (NRIDE) is introduced in a novel way to get an accurate analytical solution. This technique is an elegant combination of theLaplace transform, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has also been established that (LT

Background: Inflammation of the brain parenchyma brought on by a virus is known as viral encephalitis. It coexists frequently with viral meningitis and is the most prevalent kind of encephalitis. Objectives: To throw light on viral encephalitis, its types, epidemiology, symptoms and complications. Results: Although it can affect people of all ages, viral infections are the most prevalent cause of viral encephalitis, which is typically seen in young children and old people. Arboviruses, rhabdoviruses, enteroviruses, herpesviruses, retroviruses, orthomyxoviruses, orthopneumoviruses, and coronaviruses are just a few of the viruses that have been known to cause encephalitis. Conclusion: As new viruses emerge, diagnostic techniques advan

Deep learning techniques are applied in many different industries for a variety of purposes. Deep learning-based item detection from aerial or terrestrial photographs has become a significant research area in recent years. The goal of object detection in computer vision is to anticipate the presence of one or more objects, along with their classes and bounding boxes. The YOLO (You Only Look Once) modern object detector can detect things in real-time with accuracy and speed.  A neural network from the YOLO family of computer vision models makes one-time predictions about the locations of bounding rectangles and classification probabilities for an image. In layman's terms, it is a technique for instantly identifying and recognizing

Deep learning techniques are used across a wide range of fields for several applications. In recent years, deep learning-based object detection from aerial or terrestrial photos has gained popularity as a study topic. The goal of object detection in computer vision is to anticipate the presence of one or more objects, along with their classes and bounding boxes. The YOLO (You Only Look Once) modern object detector can detect things in real-time with accuracy and speed. A neural network from the YOLO family of computer vision models makes one-time predictions about the locations of bounding rectangles andclassification probabilities for an image. In layman's terms, it is a technique for instantly identifying and rec

The goal of the research is to theoretically establish the variable of brilliant leadership and explain the importance of this variable and the philosophical orientation of researchers in taking it as an original variable in their research as an independent variable. The descriptive approach and theoretical framing of brilliant leadership were followed. We relied on secondary data represented by books, dissertations, dissertations, scientific research, and the information network (the Internet) as a tool for collecting data. The scientific value was represented by the importance of consolidating brilliant leadership and reviewing the most important things that were confirmed by the research and studies that dealt with this research.