Journal of Computational Mathematics and Computer Modeling with Applications
Volume:2 Issue: 1, Winter and Spring 2023

The current research develops a derivative-free family without memory methods. The proposed method consisting of two steps and one parameter for solving nonlinear equations is brought forward.\,The basin of attraction of the proposed methods has investigated using different weight functions.\,Numerical examples are experimented with to check the performance of the proposed schemes. Furthermore, the theoretical order of convergence is confirmed on the experiment work.

Covid-19 disease is a respiratory illness caused by SARS-Cov-2 and poses a serious public health risk. It usually spread from person-to-person. The fractional- order of covid-19 was determined and basic reproduction number using the next generation matrix was calculated. The stability of disease-free equilibrium and endemic equilibrium of the model were investigated. Also, sensitivity analysis of the reproduction number with respect to the model parameters were carried out. It was observed that in the absence of infected persons, disease free equilibrium is achievable and is asymptotically stable.Numerical simulations were presented graphically. The results of the model analysis indicated that $R_{0}$ $\mathrm{<}$ 1 is adequate enough to reducing the spread of disease and disease persevere in the population when $R_{0}$ $\mathrm{>}$ 1 The numerical results showed that effective vaccination of the population helps in curtailing the spread of the viral disease.In order to know whether the disease may die out or persist, basic reproduction number, $R_{0}$ was obtained using Next Generation Matrix Method. It was observed that the value of $R_{0}$ is high when the depletion of awareness programme is high while the value of $R_{o}$ is very low when the rate of implementation of awareness programme is high. So, neglecting the implementation of awareness program can have serious effect on the population. The model shows the implementation of awareness program is the key eradication to the pandemic.

Determining a player's proper position in football is critical for maximizing their impact on the field. In this study, we propose a scientific and analytical approach to address this issue using machine learning models. We use the FIFA dataset to identify the correct positions for players and show that the logistic regression model provides the most accurate predictions, with an average accuracy of 99.84\% on test data across the all positions. To further refine player positioning, we use the Recursive Feature Elimination (RFE) method to identify the most important features associated with each position. The top five features identified through RFE are used to evaluate players' suitability for their correct positions and we illustrate that the average Mean Squared Error (MSE) is 1.166 on a scale of 100, indicating high accuracy in predicting their suitability scores. Overall, our results suggest that the logistic regression model is an effective tool for accurately determining player positions, and that the selected features can be used to evaluate players' suitability for a given position with high accuracy. Our approach provides a data-driven solution to help teams make better decisions in player selection and positioning, potentially leading to improved team performance and success.

This paper presents a novel approach for tackling the Lane-Emden equation, a significant nonlinear differential equation of paramount importance in the realms of physics and astrophysics. We employ the Chimp optimization algorithm in conjunction with Chebyshev polynomials to devise an innovative solution strategy. Inspired by the behavioral patterns of chimpanzees, the Chimp algorithm is harnessed to optimize the Chebyshev polynomial approximations, thereby transforming the Lane-Emden equation into an unconstrained optimization problem. Our method's effectiveness is demonstrated through a series of numerical experiments, showcasing its capability to precisely solve the Lane-Emden equation across various polytropic indices.

This paper addresses the escalating global mental health crisis, particularly accentuated by the COVID-19 pandemic, by proposing a robust solution for the automated detection of depression. Leveraging the DAIC-WOZ dataset, a collection of clinical interviews and survey evaluations from over a hundred individuals, the study employs machine learning algorithms to automate and enhance depression recognition. The performance of the proposed models is rigorously evaluated using key metrics, including root mean square error (RMSE) and mean absolute error (MAE). A significant innovation is introduced with the incorporation of a novel attention fusion network, allowing the integration of features extracted from diverse modalities such as video, text, and audio. The study places a distinctive emphasis on intramodality connection, elucidating the intricate interactions among features within and across modalities. Structured into two pivotal sections, the first reviews existing approaches to automatic depression recognition, exploring associated areas and commonly employed modalities. The second section focuses on methodologies related to visual and audio modalities, laying the foundation for the proposed algorithm. The research strives to contribute valuable insights to the field, offering an effective approach to depression recognition through the integration of multi-modal machine learning techniques. The potential ramifications extend to more accurate mental health assessments and the development of targeted intervention strategies. This study emerges as a timely and crucial endeavor to address the pressing challenges posed by the global mental health crisis.

This paper focuses on deriving analytical solutions for three-dimensional projectile motion and investigating numerical approaches for handling these solutions. We derive the equations of projectile motion using both classical and fractional calculus, considering scenarios with and without air resistance. We analyze the characteristics of the projectile's trajectory in both classical and fractional scenarios, providing a comparative study between them. Additionally, we propose an extrapolation method tailored to the nature of the motion equations to estimate projectile trajectories. The accuracy of our proposed method is assessed through the absolute error between exact and numerical solutions, with numerical examples provided to validate the theoretical analysis.