Department of Mathematics.

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    The Third Romberg Extrapolate as a Numerical Integration
    (European Centre for Research Training and Development UK, 2025) Akinlabi, Grace O.
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    Shooting Method for the Solution of Nonlinear Boundary Value Problems
    (Annals of Science and Technology, 2024) Akinlabi, Grace O.; Nduka, George S.
    This work describes the shooting method for the solution of a second-order nonlinear Boundary Value Problem (BVP). This method works by first transforming each BVP into a system of Initial Value Problems (IVPs). The initial conditions associated with the IVPs are then adjusted to match the boundary conditions associated with the BVPs by making guesses or “shooting for values”. This process is repeated using the secant method to determine the right value until the initial conditions are satisfactorily closed to the boundary conditions. The IVPs are solved using the Euler method. The Euler method was chosen for this work primarily due to its simplicity and ease of implementation. An illustrative example is considered and the results obtained show the importance of the shooting method to BVPs.
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    MATHEMATICAL MODELING AND ANALYSIS OF BANK CAPITAL ADEQUACY DYNAMICS
    (Jomard Publishing, 2024) Akinlabi, Grace O.; Edeki, S. O.; Adedotun, A. F.; Khalique, Chaudry Masood
    Maintaining adequate capitalization is paramount for banks to ensure financial stability and regulatory compliance. This paper employs the Differential Transform Method (DTM) to solve a proposed dynamic model of bank capital adequacy, focusing on the relationship between a bank’s capital and its risk-weighted assets (RWAs). Three settings of RWAs growth, namely constant, linearly increasing, and exponentially increasing, are explored, with their respective parameter setups embedded. The effectiveness of the DTM is validated through comparisons of the obtained solutions with their corresponding exact solutions, demonstrating its ability to accurately simulate capital adequacy dynamics under varying RWAs growth patterns. The equilibrium analysis reveals that the steady-state level of capital adequacy is directly proportional to the bank’s assets, emphasizing the importance of asset growth for financial stability. Stability analysis indicates that a positive decay rate is crucial for resilience against perturbations. These findings underscore the application of mathematical modeling using DTM in aiding banks’ capital management strategies amidst evolving financial landscapes, ensuring they maintain adequate capital levels and respond effectively to economic shocks.
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    Solution analysis of Solow Growth Model for financial practices and applications
    (ScienceDirect Social Sciences & Humanities Open, Elsevier Ltd, 2024) Edeki, Sunday O.; Arowosegbe, Dideolu O.; Akinlabi, Grace O.; Khalique, Chaudry Masood
    Solow Growth Model (SGM) is an economic model that is exogenous in nature and examines the relationship between the output and input levels in an economy over a period of time. It projects long-term economic growth in relation to labour (population growth), savings rate, and technological development. However, traditional approaches to solving the Solow growth model may rely on complex mathematical techniques that might not give an accurate representation of real-world economic dynamics. Thus, this paper applies the Natural Decomposition Method (NDM) to the Solow growth financial model. The NDM is a numerical technique that combines the Natural Transform (NT) and the ADM-Adomian decomposition method. The NDM simplifies problem-solving by converting the original differential equations into algebraic equations as regards limitations associated with nonlinear models. From the results obtained by applying the NDM to the Solow growth financial model, researchers and policymakers can better understand the interplay between financial variables, such as savings rates, investment, and capital allocation, and their impact on economic growth dynamics, as a systematic approach to capturing the complex relationship between finance and economic development within the Solow framework is ensured. Further research and application of the NDM can contribute to advancing the knowledge of economic dynamics and support evidence-based decision-making in economic policy.
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    Iterative Method for Approximate-Analytical Solutions of Linear Schrödinger Equation
    (IOP Publishing, 2021) Akinlabi, Grace O.; Braimah, J.A.; Abolarinwa, A.; Edeki, S.O.
    In this study, the modified Picard Iterative Method (MPIM) is used to provide analytic and numerical solutions to linear Schrödinger Equations. These approximate analytical solutions for the examples under consideration are easily computed. The suggested method is employed without any transformation, discretization, linearization, or limiting assumptions. The obtained results are similar to their exact forms. As a result, the approach is highly suggested for both linear and non-linear time-space fractional partial differential models with applications in various applied disciplines.
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    Solutions of Linear Vibration Mechanical Models Using Zhou Transform Method
    (Mathematical Modelling of Engineering Problems, 2024) Akinlabi, Grace O.; Egbogho, Henry E.
    Vibration is a mechanical phenomenon that causes oscillations around an equilibrium point. Vibration is undesired in many areas, particularly engineered systems and inhabited spaces, and strategies to avoid vibration transfer to such systems have been proposed. Mechanical waves carry vibrations, and certain mechanical couplings transport vibrations more efficiently than others. By detecting equipment defects, vibration analysis (VA) in an industrial or maintenance setting seeks to save maintenance costs and downtime. Associated models from vibration settings can either be linear or nonlinear based on the modeling situation. This paper considers the Zhou Transform Method (ZTM) as a semi-analytical approach for obtaining the solutions of linear vibration mechanical models. Two illustrative examples are considered. The results obtained from the ZTM are compared with their exact forms for applicable case(s). The results show that the proposed method is very effective and reliable in obtaining approximate solutions based on the comparison.
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    Regularized Models for Fitting Zero-Inflated and Zero-Truncated Count Data: A Comparative Analysis
    (2023) Akinlabi, Grace O.; Adesina, Olumide S.; Okewole, Dorcas M.; Adedotun, Adedayo F.; Adekeye, Kayode S.; Edeki, Onos S.
    Generalized Linear Models (GLMs) are widely recognized for their efficacy in fitting count data, superior to the Ordinary Least Squares (OLS) approach. The incapability of OLS to suitably handle count data can be attributed to its tendency to overfit. This study proposes the utilization of regularized models, specifically Ridge Regression and the Least Absolute Shrinkage and Selection Operator (LASSO), for fitting count data. These models are compared to frequentist and Bayesian models commonly used for count data fitting, such as the Dirichlet prior mixture of generalized linear mixed models and the discrete Weibull. The findings reveal Ridge Regression's superiority over all other models based on the Akaike Information Criterion (AIC). However, its performance diminishes when evaluated using the Bayesian Information Criterion (BIC), even though it still outperforms LASSO. The study thereby suggests the use of regularized regression models for fitting zero-inflated count data, as demonstrated with simulated data. Further, the appropriateness of regularized zero for zero-truncated count is exemplified using life data.
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    EVALUATION OF THE IMPACT OF FORMATION CHANGES ON GOAL-SCORING POSSIBILITIES IN EUROPE’S TOP FIVE FOOTBALL LEAGUES
    (Covenant University Ota, 2025-08) OLATUNJI, Iyanuoluwa Daivd; Covenant University Dissertation
    This researchexaminestheinfluenceofadaptivetacticalformationswitchingin Europe’stopfiveleagues.Theresearchappliesextensiveevent-basedmatchdata from thetopfiveEuropeanleagues(StatsBombdataset,2015/16season)toanalyse switchesbetweenformationsandtheirinfluenceonmatchresults.Thestudyemploys Markovchains,reinforcementlearningandgametheorytomodelandanalysethe frequency andeffectivenessofformationchangesduringfootballmatchesandpro- vide relevanttacticalinsightsandsuggestions.Thefindingsrevealprofoundstrategic trends intacticalswitches,attestingtothecentralroleofresponsivenessandflexibil- ityinmatchdynamics.Themethodsintroducedinthisstudyyieldbetterresultsin terms ofthecombinationofthemodelscomparetootherexistingmethodswithsingle methodutilized.Thecombinedmethodsquantifytheprobabilitiesandtrade-offsfor variousformationchangesandthus,providebettertacticalinsight.
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    MATHEMATICAL ANALYSIS OF RUMOUR SPREADING MODEL IN SOCIAL NETWORKS
    (Covenant University Ota, 2025-08) OLOYEDE, Godliness Iyanuoluwa; Covenant University Dissertation
    The rapid spread of rumours through online social networks significantly influences public perception, decision-making, and societal stability. This study extends the traditional Susceptible-Infectious-Hibernator-Recovered (SIHR) rumour transmission model by incorporating external triggers (y) and delayed remembering mechanisms governed by a time delay (r ). The extended model captures the complex interplay between forgetting, memorydriven re-engagement, and external triggers of rumour activity. The system of delay differential equations is solved using the Fourth-Order Runge-Kutta (RK4) method implemented in Python and the Differential Transform Method (DTM) in Maple for comparative numerical analysis. A comprehensive stability analysis is conducted to identify equilibrium states and evaluate the longterm behaviour of the system under varying parameter conditions. Simulation results highlight the critical roles of remembering mechanisms, forgetting rates, and external stimuli in determining whether a rumour dies out or persists. The time-delay-dependent reproduction number is derived to identify bifurcation points and thresholds for instability. The fmdings offer practical insights into how memory and external triggers influence rumour spread, informing the design of timely and effective strategies for misinformation control in contexts such as crisis response, political communication, and public health.
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    Programme: Industrial Mathematics