This study presents a perturbed exponentially fitted collocation method for solving higher-order integrodifferential equations. The proposed method combines the strengths of exponential fitting and collocation techniques to efficiently handle the oscillatory and exponential behaviors inherent in these equations. By incorporating perturbation terms, the method enhances accuracy and stability for stiff problems. Numerical examples are solved, it is observed that the method yielded exact solution in example 4.1 and 4.2 and achieves near-machine precision (error ∼ 10⁻¹⁶) at x = 1.0 compared with Bessel polynomial Approximation Method, showcasing its potential for solving complex integrodifferential equations in various applications.

Diarrhea is responsible for killing around 525,000 children every year, even though it is preventable and treatable. More than 130 nations are affected by the illness of diarrhea. Mathematical models provide a valuable tool for understanding the dynamics of infectious diseases like diarrhea and evaluating potential control strategies. To understand its transmission dynamics in Bangladesh, this study develops a Susceptible-Infectious-Recovered (SIR) mathematical model that incorporates both the human (host) and housefly (vector) populations. The model consists of five nonlinear ordinary differential equations (ODEs). We analyze the model to determine its equilibrium points and the basic reproduction number (R₀ ). Using demographic and epidemiological parameters for Jashore and Khulna, Bangladesh, we calculate the basic reproduction number to be R₀=1.35. This value, being greater than 1, indicates that the disease-free state is unstable and predicts a stable endemic equilibrium where diarrhea persists in the population. Numerical simulations for Khulna and Jashore illustrate this endemic dynamic, showing a decline in initial infections followed by long-term persistence. The findings confirm the model's utility in explaining the endemic nature of diarrhea in the region and highlight that interventions targeting vector (housefly) control are essential for effective public health strategies.

The Black-Scholes equation plays an important role in financial mathematics for the evaluation of European options. It is a fundamental PDE in financial mathematics, models the price dynamics of options and derivatives. While a closed-form of analytical solution exists for European options, numerical methods remain essential for validating computational approaches and extending solutions to more complex derivatives. This study explores and compares various numerical techniques for solving the Black-Scholes partial differential equation, including the finite difference method (explicit, implicit, and Crank-Nicolson schemes), and Monte Carlo simulation. Each method is implemented and tested against the analytical Black-Scholes formula to assess accuracy, convergence, and computational efficiency. The results demonstrate the strengths and limitations of each numerical approach, providing insights into their suitability for different option pricing scenarios. This comparative analysis highlights the importance of method selection in practical financial modeling applications.

Blockchain technology has emerged as a pivotal innovation across multiple sectors due to its decentralized nature, secure transaction processing, and transparency. Central to blockchain operations are cryptographic hashing algorithms like SHA256 and Scrypt, which play a crucial role in ensuring transaction integrity and security. This study conducts a comprehensive benchmarking analysis of SHA256 and Scrypt, focusing on their performance in blockchain block discovery, specifically evaluating hashing speed and block discovery probability. SHA256, known for its high hashing speed, demonstrated rates reaching 101.111 kH/s during a 10-hour test, whereas Scrypt performed at a slower average speed of 9 kH/s. However, Scrypt exhibited a higher probability of block discovery, achieving up to 8.18%, significantly surpassing SHA256's near-zero probability under similar conditions. Tests across various CPUs underscore these differences: SHA256 excels in raw hashing speed, while Scrypt’s memory-intensive design offers greater ASIC resistance and a higher likelihood of block discovery, especially in environments that demand enhanced security. These findings highlight the importance of choosing an algorithm aligned with the specific requirements of a blockchain application, balancing speed, security, and resistance to specialized hardware attacks. The study suggests that hybrid approaches combining SHA256’s speed with Scrypt’s security features could maximize both efficiency and security, contributing valuable insights into the ongoing optimization of blockchain technology.

Computer-Based Testing (CBT) has gained prominence in Nigeria due to its efficiency and scalability in evaluating students across various educational institutions. However, various forms of exam cheating, such as candidate swapping and unauthorised assistance, threaten its integrity. This research explores the application of Convolutional Neural Networks (CNNs) for identity verification in Nigerian CBT environments and presents a CNN-driven facial biometric model based on the findings. The model extracts facial features of examinees from real-time videos of CBT exam sessions, and it compares them with pre-registered data to verify test takers' identities, as well as to detect and report instances of candidate swapping and unauthorised assistance during the ongoing exam. The model is trained on diverse datasets like VGGFace2 and CASIA African Face Dataset to enhance fairness and accuracy for African demographics. This ensures effectiveness in Nigerian Computer-Based Testing (CBT) and local contexts. Evaluation of the model and its comparative analysis with existing systems and other biometric methods were performed. The assessment involved 2,000 genuine and 3000 impostor samples, achieving 99.52% accuracy with high precision and recall of 0.998 and 0.99, respectively. The results demonstrate the model’s high accuracy, low false acceptance, and minimal false rejection rates, and highlight the model’s viability in maintaining exam integrity and accessibility.