Author(s): Ibrahim Salihu, Ayinde Muhammed Abdullahi, Azeez Aderemi Rasaq and Oyedepo Taiye

Abstract: In this research, our focus was on deriving an implicit linear multistep method for the direct integration of Initial Value Problems (IVPs) involving second-order ordinary differential equations of the form y'' = f(x, y, y'), employing the Taylor series expansion. Through the analysis and implementation of the Taylor series expansion, we determined the values of and . To evaluate the accuracy of the proposed method, we conducted tests using both linear and non-linear second-order ordinary differential equations. The obtained results clearly demonstrated that the proposed method exhibited superior accuracy compared to some existing numerical methods in terms of consistency and convergence. These findings highlight the effectiveness of the proposed method in providing more accurate solutions for second-order ordinary differential equations. The utilization of the Taylor series expansion as an analytical and implementation tool in this research proved to be successful in enhancing the accuracy and reliability of the numerical method. This research contributes to the advancement of numerical techniques for addressing mathematical models in various scientific and engineering domains.

Pages: 11-15 | Views: 208 | Downloads: 87

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