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Mamadu-Njoseh polynomial-based Projected Heun method for solving initial value problems
International Journal of Statistics and Applied Mathematics · 2026 · Vol. 11(5) · pp. 16–27
Ebimene James Mamadu(Delta State University)Jude Chukwuyem Nwankwo(University of Delta Agbor)Inonoje S.O. EmmanuelOtaide I. JacksonEbikonbo-Owei Anthony Mamadu(Delta State University)Amaka Joyce MamaduIrerhievwie Oghenetega Stephen(Southern Delta University, Ozoro)Efe Kenneth JohnsonEwoma Justice AluyaHenrietta Ify OjarikreIgnatius Nkonyeasua Njoseh(Delta State University)
Abstract
This paper introduces a Projected Heun Scheme (PHS) based on Mamadu-Njoseh polynomials for solving linear and nonlinear Initial Value Problems (IVPs). The scheme preserves the second-order convergence of the classical Heun method but achieves faster convergence and improved accuracy, particularly for nonlinear and oscillatory systems. A detailed stability analysis confirms its wider stability region, making it a robust and efficient tool for high-precision numerical solution of IVPs in computational science and applied mathematics.
Numerical methods for differential equationsMathematical functions and polynomialsMathematical and Computational Methodsinitial value problemsoscillatory systemsnonlinear initial value problemsstability analysis
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