In this paper, we study the influence of applying the well-known finite differences method on medical and physical images. These images will be used as coefficients in the steps of the solution after the images being imported and converted to arrays. The aim of the study is to show and analyze the changes that could happen to images for the sake of an enhancement. Experiments of one dimension and two dimensions will be illustrated by applying the explicit and the implicit methods using MATLAB to explain the way of how these methods affect images. Furthermore, we will study and measure the quality of the proposed images in each phase of the experiments using statistical metrics such as PSNR (Peak Signal to Noise Ratio), MSE (Mean Squared Error), MD (Maximum Difference) and some other statistical metrics.

In this paper, we present an intensive investigation of the finite volume method (FVM) compared to the finite difference methods (FDMs). In order to show the main difference in the way of approaching the solution, we take the Burgers equation and the Buckley–Leverett equation as examples to simulate the previously mentioned methods. On the one hand, we simulate the results of the finite difference methods using the schemes of Lax–Friedrichs and Lax–Wendroff. On the other hand, we apply Godunov’s scheme to simulate the results of the finite volume method. Moreover, we show how starting with a variational formulation of the problem, the finite element technique provides piecewise formulations of functions defined by a collection of grid data points, while the finite difference technique begins with a differential formulation of the problem and continues to discretize the derivatives. Finally, some graphical and numerical comparisons are provided to illustrate and corroborate the differences between these two main methods.

The oscillation of a class of fourth-order nonlinear damped delay differential equations with distributed deviating arguments is the subject of this research. We propose a new explanation of the fourth-order equation oscillation in terms of the oscillation of a similar well-studied second-order linear differential equation without damping. The extended Riccati transformation, integral averaging approach, and comparison principles are used to provide some additional oscillatory criteria. An example demonstrates the efficacy of the acquired criteria.

Cancer is a noncommunicable chronic disease that indistinctly affects people of any nationality, race, ethnicity, age, or social class. Because of its unpredictability, receiving the diagnosis of this disease is almost always alarming for the patient. Breast cancer, especially among women, occupies a prominent position in this ranking. However, if diagnosed early, there is an excellent chance of a cure. In this sense, digital technologies have been advancing at an increasingly fast pace to support the early diagnosis of the disease. Clinical analysis of breast cancer is commonly performed using diagnostic imaging. One of the most used exams considered the main one for the early detection of this type of cancer is mammography. This exam allows the visualization of breast tissue from image screening using X‐rays. In this sense, the use of computational techniques is essential to assist medical professionals in diagnosing this disease, thus making prevention and early diagnosis even more effective in the current context. The present work is limited to the use of digital technologies (image processing and artificial intelligence) that cooperate with the early diagnosis of breast cancer, which supports the medical professional to analyze images and be able to diagnose, from an early stage, the emergence of breast cancer of the disease, significantly increasing the chances of curing it. It can be gathered from this research how the discovery of X‐rays and the growth in this sector combined with cutting‐edge technology have benefitted in the early detection of the disease and even offered the cure of many cases.

We studied the asymptotic behavior of fourth-order advanced differential equations of the form ${\left(a\left(\upsilon \right){\left(w^{\prime \prime \prime }\left(\upsilon \right)\right)}^{\beta }\right)}^{\prime }+q\left(\upsilon \right)g\left(w\left(\delta \left(\upsilon \right)\right)\right)=0$. New results are presented for the oscillatory behavior of these equations in the form of Philos-type and Hille–Nehari oscillation criteria. Some illustrative examples are presented.