A Unified (v, w)–Strongly Convex Simpson-Type Framework for Non-Quadratic RLC Impedance Models in Energy Distribution Networks

This paper presents generalized Simpson-type inequalities for differentiable functions whose derivatives satisfy a pairwise strong convexity condition. The proposed bound extends Samet’s (v,w) –convex framework by incorporating an explicit curvature term, producing tighter and structure-aware estimates without requiring higher-order smoothness. The analysis is applied to the non-quadratic parallel RLC load-impedance model, a primary source of nonlinearity in electrical distribution networks. Using frequency-domain characterization and admissible weighting functions, we show that the magnitude of the derivative of the RLC impedance is strongly convex, leading to sharper integral bounds and reliable error certification. Numerical experiments demonstrate that the proposed framework yields conservative yet auditable estimates and provides a practical tool for frequency-dependent computations in applications where certified numerical accuracy is essential.