Unilag Journal of Mathematics and Applications

PERFORMANCE EVALUATION OF A COMPUTATIONAL BLOCK METHOD FOR SOLVING QUADRATIC RICCATI DIFFERENTIAL EQUATIONS: A NUMERICAL VALIDATION AND COMPARATIVE ANALYSIS

MUSILIU TAYO RAJI — 2026-03-09

This study presents a computational block method derived through interpolation and collocation using power series polynomials for solving quadratic Riccati differential equations (QRDEs). A rigorous analysis of the method's core properties including order, consistency, and stability confirms its theoretical soundness. The method's performance was evaluated by applying it to three benchmark QRDEs. Numerical results demonstrate that the proposed method achieves significantly higher accuracy compared to several existing techniques documented in the literature. The study concludes that the computational block method is an efficient and reliable numerical tool for solving QRDEs, offering superior precision and convergence characteristics.

THE GENERALISED HERMITE REGRESSION MODEL: A ROBUST FRAMEWORK FOR EXTREME NONLINEAR DATASETS

KEHINDE ABAYOMI TITILOYE — 2026-03-09

Nonlinear regression modelling is a fundamental problem in econometrics and applied statistics, particularly for datasets exhibiting heavy tails, skewness, and volatility clustering. Such features are prevalent in many empirical applications and frequently violate the assumptions underlying classical linear regression methods. The central hypothesis of this study is that a regression framework based on orthogonal polynomial expansions can provide improved stability and predictive performance in the presence of pronounced nonlinear behaviour. The motivation for this work arises from the limitations of Ordinary Least Squares regression, which relies on linearity and distributional regularity, and from the instability of standard polynomial regression when applied to heavy-tailed data. To address these issues, the Generalised Hermite Regression Model (GHRM) is proposed by embedding Hermite polynomial expansions into a regression structure, enabling higher-order nonlinear dependencies to be modelled while preserving key theoretical properties. A numerical experiment based on a simulated dataset of 10,000 observations exhibiting nonlinear and heavy-tailed behaviour is conducted to evaluate the proposed model. The GHRM is assessed in comparison with Ordinary Least Squares and cubic polynomial regression using forecasting accuracy measures and information criteria. The results show that Ordinary Least Squares performs poorly under nonlinear conditions, while both polynomial regression and the GHRM achieve substantial improvements in predictive accuracy. Although the two nonlinear models produce comparable numerical results under the cubic specification, the GHRM demonstrates superior structural stability due to the orthogonality of the Hermite basis. These findings establish the GHRM as a robust and scalable framework for modelling nonlinear datasets with complex distributional characteristics.

NUCLEAR IDENTIFICATION OF EXTRA LOOP IDENTITIES OF SECOND BOL-MOUFANG TYPE WITH APPLICATIONS TO SECURE INFORMATION ENCODING

OLUFEMI GEORGE — 2026-03-09

Drpal and Jedlika identified several loop identities, including both BolMoufang and non-BolMoufang varieties through their nuclei. Among these are the extra identities. Subsequently, George and Jaiyeola developed a generalized nuclear identification scheme for identities of the second BolMoufang type. While they discovered twelve new loop identities, their approach did not establish a nuclear identification for the extra identities. This left open the question of whether extra-type identities admit nuclear identification in the second BolMoufang setting. In this paper, we introduced three new loop identities (SBME, SBRE, SBLE) of second BolMoufang type. In particular, we show that an extra loop of second BolMoufang type is nuclear- identifiable if it can be expressed as autotopisms α^є ∗ η(x)α^c ∗ ξ(x)αⁿ ∗ χ(x)α^ψ ∗ ζ(x) and satisfies an identity (η, ξ, χ, ζ, ϵ, ω, κ, ψ) such that η = χ /= ξ /= ζ. Furthermore, we show that the newly introduced extra identities of second BolMoufang type are equivalent to the extra identities of first BolMoufang type. Beyond the algebraic characterization, we illustrate how nuclear identification codes can inspire secure information encoding schemes, where loop identities serve as human-recognizable keys for controlled access in sensitive communication environments.

SEMI-ANALYTICAL ITERATIVE METHODS FOR SOLVING TIME-FRACTIONAL RICCATI DIFFERENTIAL EQUATION

KAZEEM IYANDA FALADE — 2026-03-09

In this paper, two semi-analytical methods for solving the time-fractional Riccati differential equation, the homotopy perturbation method (HPM) and the modified new iterative method (MNIM), are employed to solve the time-fractional Riccati equation, which is characterized by its nonlinear and fractional-order nature, and serves as a fundamental model in mathematical physics and engineering processes involving memory and hereditary properties. By incorporating the Caputo fractional derivative, the study captures the nonlocal temporal dynamics of the system. The MNIM is formulated to enhance convergence and minimize computational complexity, while HPM is utilized to construct an approximate analytical series solution without linearization or discretization. Both methods yield rapidly convergent series solutions that approximate the exact analytical solution with high accuracy. We considered two test cases, and the results demonstrated the efficiency, simplicity, and robustness of the proposed methods for various fractional orders, establishing both methods as powerful tools for fractional nonlinear differential equations in applied sciences and engineering. The paper lies in applying semi-analytical iterative methods tailored to the time-fractional Riccati differential equation, providing accurate approximate solutions with reduced computational complexity.

DEVELOPMENT OF A CONTINUOUS MULTI-STEP ONE-FOURTH STEP HYBRID SCHEME FOR THIRD-ORDER IVP IN ORDINARY DIFFERENTIAL EQUATIONS

OLUWASAYO ESTHER TAIWO — 2026-03-09

This study introduces a hybrid block approach for the approximate solution of initial value problems involving third-order ordinary differential equations. The formulation of the method employs orthogonal and Chebyshev polynomials as basis functions, with its performance enhanced through the incorporation of off-step points. This modification is aimed at achieving zero-stability while maintaining high computational accuracy. Several numerical experiments are carried out to demonstrate the methods effectiveness, and the results confirm its reliability and efficiency in solving such problems.

C*-ALGEBRA-VALUED b-METRIC-LIKE SPACE AND SOME FIXED POINT THEOREMS

ZULAIHATU TIJJANI AHMAD — 2026-03-09

In this article, we initiate the notion of C^∗-algebra valued b- metric-like space. The Banach and Kannan fixed point results are examined in such space. Contrasting examples are formulated to show that the proposed ideas herein are novel and extend some important significant results in the literature.

AN APPLICATION OF BANACH’S CONTRACTION PRINCIPLE TO THE NUMERICAL TREATMENT OF NONLINEAR VOLTERRA-FREDHOLM EQUATIONS IN HEALTH DOMAINS

IKENNA STEPHEN OKEKE — 2026-03-09

This paper investigates the numerical approximations of nonlinear Volterra-Fredholm equations, focusing on their bounded solutions over specified regions. The research employed the Banach contraction principle to prove the existence of a unique solution in the space of continuous functions. The integral equations were formulated to model complex interactions in various applications, particularly infectious disease dynamics. Also, some key parameters, like the kernel functions and scalar multipliers were analyzed to ascertain that the contraction mappings conditions are satisfied. The Picard iteration was used to approximate solutions, proving convergence and stability results. The findings showed significance of these mathematical models in dynamic systems and optimizing treatment in healthcare. This work contributes to the existing literature on nonlinear integral equations.

ENSEMBLE-BASED FRAUD DETECTION IN NIGERIAN BANKING: A SYNTHETIC DATA BENCHMARK AND COST-SENSITIVE ANALYSIS GBOLAHAN ADENIRAN IDOWU∗ AND JOSIAH ENDURANCE OWOLABI ABSTRACT. Fraud detection in Nigerian banking is critically hampered by a scarcity of authen

GBOLAHAN ADENIRAN IDOWU — 2026-03-09

Fraud detection in Nigerian banking is critically hampered by a scarcity of authentic transaction data for model development, a challenge exacerbated by the rapid growth of digital payments. To address this foundational data gap, this study introduces a novel, high- fidelity synthetic benchmark dataset of 1,000,000 financial transactions, meticulously calibrated to reflect the fraud patterns reported by the Nigeria Inter-Bank Settlement System (NIBSS). Using this dataset, we develop a comprehensive analytical framework to evaluate the economic efficacy of advanced machine learning models. The results demonstrate a substantial potential for fraud loss reduction: optimized Random Forest models achieved a 69.1% decrease in simulated fraud-related costs (from 81.8M to 25.2M) while maintaining perfect precision. Alternatively, XGBoost delivered superior recall (74.6%) with an F1-score of 0.854, providing a strategic option for institutions prioritizing fraud detection rates. A SHAP analysis identified transaction amount and associated behavioral features as the strongest fraud indicators and highlighted Web and Mobile channels as requiring enhanced monitoring. This paper makes three principal contributions: the first publicly available, NIBSS-calibrated fraud detection dataset for Nigeria, addressing a pivotal data scarcity in African financial research; empirically validated evidence that ensemble methods, combined with threshold optimization, can reduce fraud costs by up to 69%; and actionable implementation guidelines for Nigerian banks operating within existing regulatory compliance frameworks. The synthetic data methodology offers a replicable and privacy- preserving blueprint for other emerging markets facing similar constraints on data access and availability.