Orthogonality-Preserving Cubic Spline Formulation Using Mamadu-Njoseh Polynomials

Objectives This study aims to develop an orthogonality-preserving cubic spline formulation using Mamadu–Njoseh polynomials as basis functions, with the objective of improving numerical stability, computational efficiency, and accuracy in spline-based interpolation. Material and Methods The proposed approach reformulates classical cubic spline segments by expressing them in terms of Mamadu–Njoseh polynomial bases. The formulation explicitly incorporates the orthogonality and weighted integration properties of these polynomials while maintaining standard interpolation constraints and boundary conditions. Analytical construction and theoretical considerations are employed to ensure consistency with the fundamental behavior of classical cubic splines. Results The resulting spline formulation successfully preserves orthogonality within each spline segment and demonstrates enhanced numerical stability and computational efficiency compared to standard cubic spline methods. The use of Mamadu–Njoseh polynomials improves accuracy while retaining the smoothness and continuity properties characteristic of classical cubic splines. Conclusion The orthogonality-preserving cubic spline formulation presented in this paper offers a robust and reliable framework for scientific computing and engineering applications. By combining the smoothness of classical cubic splines with the structured advantages of Mamadu–Njoseh orthogonal polynomial bases, the method provides an effective alternative for accurate and stable interpolation.