This paper proposes a unified operator-theoretic framework for analyzing the Finite Difference Method (FDM) and the Variational Iteration Method (VIM) for solving nonlinear second-order boundary value problems (BVPs). The VIM iteration is interpreted as a Picard-type fixed-point iteration in a Banach space, and a computable a priori error bound is established under a Lipschitz condition on the nonlinearity. Concurrently, FDM is treated as a finite-rank projection method, and its convergence is demonstrated via consistency and stability. The main contribution of this work is a novel hybrid a posteriori error estimator that uses the continuous VIM iterate to bound the global discretization error of the FDM solution without requiring additional PDE solves or mesh-doubling, requiring only the VIM iteration already computed as part of the error estimation process. Unlike traditional residual-based estimators, the proposed estimator relies solely on the discrepancy between the smooth semi-analytical approximation and the discrete numerical solution. Theoretical convergence rates and the efficiency of the estimator are validated through numerical experiments on a nonlinear BVP with a known exact solution and a non-solvable linear BVP. The results indicate that the hybrid estimator provides a reliable and computationally efficient indicator for adaptive mesh refinement.
A commensurate Caputo model of HIV infection of CD4+ T cells is analysed by separating biologically admissible equilibria from algebraic roots. Building on the fractional model of Okeke et al. [1] and the hybrid activation construction of Essang et al. [2], this study introduces bounded neural modifiers of infection and viral production rates. Explicit equilibrium expressions and an infection threshold are derived. The disease-free equilibrium is locally asymptotically stable below the threshold, while a unique positive endemic equilibrium exists and is locally asymptotically stable above it for every common order in $(0,1]$. A recalculation using the parameter values reported in [1] produces a stable endemic equilibrium, contrary to the published numerical classification. A conservative bound on neural modifiers provides a sufficient condition for local disease-free stability across fixed covariate settings. A completed numerical study reports dimensionless fractional trajectories, threshold surfaces, Jacobian spectra and time-step refinement. These results concern mathematical equilibria rather than clinical treatment efficacy.
Programme accreditation by the National Universities Commission (NUC) is the main external quality assurance mechanism in Nigerian universities, but it is periodic and retrospective: weaknesses are usually discovered during the visit rather than before it. This study aimed to develop and evaluate a machine-learning (ML) framework that predicts accreditation outcomes from routinely collected pre-visit indicators so that institutions can remediate deficiencies early. Because programme-level accreditation records are not publicly available, we built a reproducible synthetic panel of 4,321 accreditation visits to 1,515 programmes in 149 simulated universities (2014–2024), with outcomes (full, interim, denied) generated by NUC-style scoring rules. Fifteen indicators covering staffing, curriculum, facilities, library, funding, research and employer rating, together with ownership, discipline and prior status, were used as predictors. Logistic regression (LR), support vector machine, multilayer perceptron, random forest and extreme gradient boosting (XGBoost) were trained on 2014–2021 visits with university-grouped cross-validation and tested on 2022–2024 visits. LR performed best on the temporal test set (accuracy 0.773; macro-F1 0.708, 95% CI 0.669–0.744; area under the curve [AUC] 0.908), exceeding a prior-status rule (macro-F1 0.537). For the binary task of identifying programmes at risk of not receiving full accreditation, LR achieved an AUC of 0.900 and good calibration; the 20% of programmes with the highest predicted risk included 52 of the 53 denied programmes. Proportion of PhD-holding staff and laboratory provision were the most influential predictors. ML-based risk scoring could support continuous, pre-emptive quality monitoring, but validation on real NUC data is required before operational use.
