Copyright © 2026 Authors retain the copyright of this article. This article is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

@article{189597,
        author = {Akhanolu, Aziegbe Gilbert and Ebhohimen, Fidelis},
        title = {A Parameter-Dependent Second-Derivative General Linear Method with Nearly Runge–Kutta Stability},
        journal = {International Journal of Innovative Research in Technology},
        year = {2025},
        volume = {12},
        number = {7},
        pages = {7193-7196},
        issn = {2349-6002},
        url = {https://ijirt.org/article?manuscript=189597},
        abstract = {This paper presents already derived parameter-dependent second-derivative general linear method (SD-GLM) for the numerical solution of ordinary differential equations (ODEs) and establishing the method with nearly almost Runge-Kutta stability properties. The proposed method will be known as the parameter dependent second derivative general linear method (PD-SDGLM) with nearly almost Runge-Kutta (NAR-K) stability and it incorporates both the first and second derivatives of the differential function and depends on adjustable parameters that enhance accuracy and stability. This is one of the possible generalizations of the classical second derivative Runge-Kutta method (SD-RKM). Order conditions are derived up to the fourth order through Taylor series expansion, and a general form of the amplification matrix is established for stability analysis using the Dahlquist test equation. By appropriate parameter selection, the method achieves “nearly almost Runge–Kutta stability,” characterized by large regions of absolute stability. The resulting framework generalizes multi-derivative general linear methods and provides a flexible foundation for constructing high-order, stiffly-stable time integrators.},
        keywords = {Parameter dependent, Second derivative, general linear method, nearly almost Runge-Kutta stability.},
        month = {December},
        }