Hybrid Numerical Method with Block Extension for Direct Solution of Third Order Ordinary Differential Equations

Duromola, M. K. and Momoh, A. L. (2019) Hybrid Numerical Method with Block Extension for Direct Solution of Third Order Ordinary Differential Equations. American Journal of Computational Mathematics, 09 (02). pp. 68-80. ISSN 2161-1203

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Abstract

This paper focuses on the development of a hybrid method with block extension for direct solution of initial value problems (IVPs) of general third-order ordinary differential equations. Power series was used as the basis function for the solution of the IVP. An approximate solution from the basis function was interpolated at some selected off-grid points while the third derivative of the approximate solution was collocated at all grid and off-grid points to generate a system of linear equations for the determination of the unknown parameters. The derived method was tested for consistency, zero stability, convergence and absolute stability. The method was implemented with five test problems including the Genesio equation to confirm its accuracy and usability. The rate of convergence (ROC) reveals that the method is consistent with the theoretical order of the proposed method. Comparison of the results with some existing methods shows the superiority of the accuracy of the method.

Item Type: Article
Subjects: GO STM Archive > Mathematical Science
Depositing User: Unnamed user with email support@gostmarchive.com
Date Deposited: 19 Jun 2023 07:28
Last Modified: 24 Jul 2024 09:32
URI: http://journal.openarchivescholar.com/id/eprint/1152

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