On the Efficiency of a One-Fifth Step Hybrid Block Method for the Numerical Solution of Second-Order Ordinary Differential Equations
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Page Numbers:
414-426
Digital Object Identifier:
10.58578/mjms.v3i2.5497
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Authors:
Oluwasayo Esther Taiwo1* 
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Abstract
In this paper, hybrid methods for solving second-order ordinary differential equations with a one-fourth step length were developed. This was accomplished using interpolation and collocation techniques. The methods were evaluated based on the properties of linear multistep methods and were found to be zero-stable, consistent, and convergent, exhibiting a favorable region of absolute stability. The proposed methods were implemented for second-order ordinary differential initial value problems. The performance of the new methods demonstrated superiority over previously developed methods in the literature, as evidenced by the resolution of five numerical examples. The results were presented in tabular form.
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References
Adeniyi, R. B., & Alabi, M. O. (2007). Continuous formulation of a class accurate implicit linear multi-step methods with Chebyshev basis function in a collocation technique. Journal of Mathematical Association of Nigeria (ABACUS), 34(2A), 58–77.
Adeyefa, O. T. (2013). Collocation approach for continuous hybrid block methods for second order ordinary differential equations with Chebyshev basis function (Unpublished doctoral dissertation). University of Ilorin, Ilorin, Nigeria.
Areo, E. A., & Rufai, M. A. (2016). Develop a new uniform fourth order one-third step continuous block method for the direct solution. British Journal of Mathematics & Computer Science, 15(4), 1–12.
Areo, E. A., Ademiluyi, R. A., & Babalola, P. O. (2008). Accurate collocation multi-step methods for integration of first order ordinary differential equations. International Journal of Computer Mathematics, 2(1), 15–27.
Anake, T. A. (2011). Continuous implicit hybrid one-step methods for solution of initial value problems of general second order ordinary differential equation (Unpublished doctoral dissertation). Covenant University, Ota, Nigeria.
Awoyemi, D. O. (1992). On some continuous linear multistep methods for initial value problems (Unpublished doctoral dissertation). University of Ilorin, Ilorin, Nigeria.
Onumanyi, P., Awoyemi, D. O., Jator, S. N., & Sirisena, U. W. (1994). New linear multi-step methods with continuous coefficients for first order initial value problem. Journal of the Nigerian Mathematical Society, 13, 37–51.
Odejide, S. A., & Adeniran, A. O. (2012). A hybrid linear collocation multi-step scheme for solving first order initial value problems. Journal of the Nigerian Mathematical Society, 31, 229–241.
Ramos, H., Mehta, S., & Vigo-Aguiter, J. (2016). A unified approach for k-step block Falkner methods for solving general second-order problems in ODEs. Journal of Computational and Applied Mathematics. https://doi.org/10.1016/j.cam.2015.12.018