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@article{189593,
        author = {Akhanolu, Aziegbe Gilbert and Ebhohimen, Fidelis},
        title = {Second Derivative Parameter Dependent General Linear Method for stiff ODEs},
        journal = {International Journal of Innovative Research in Technology},
        year = {2025},
        volume = {12},
        number = {7},
        pages = {7163-7175},
        issn = {2349-6002},
        url = {https://ijirt.org/article?manuscript=189593},
        abstract = {The development of efficient and stable numerical methods for the integration of stiff ordinary differential equations (ODEs) remains a central challenge in computational mathematics. This paper introduces and analyzes Second Derivative Parameter Dependent General Linear Methods (SDPD-GLMs), a novel class of general linear methods that incorporate both the first and second derivative information of the underlying system together with free parameters for optimization. The inclusion of second derivative terms enhances the accuracy of the scheme, while the parameter dependence allows flexibility in optimizing stability, error control, and implementation efficiency. Order conditions are derived through Taylor series expansion and algebraic analysis, establishing a systematic framework for constructing high-order methods. The stability properties of the proposed schemes are investigated, with emphasis on A-stability and L-stability criteria relevant for stiff problems. Numerical experiments on benchmark initial value problems demonstrate that SDPD-GLMs achieve improved accuracy and efficiency compared with existing Runge–Kutta and traditional general linear methods, particularly in the stiff regime. The results highlight the potential of SDPD-GLMs as a robust tool for solving a broad class of stiff ODEs, providing a balance between high accuracy, computational efficiency, and stability.},
        keywords = {stiff ordinary differential equations, second derivative parameter dependent, general linear methods, stability, accuracy, RKM.},
        month = {December},
        }