A class of single-step hybrid block methods with equally spaced points for general third-order ordinary differential equations

Maduabuchi Gabriel Orakwelu; Olumuyiwa Otegbeye; Hermane Mambili-Mamboundou

doi:10.46481/jnsps.2023.1484

Authors

Maduabuchi Gabriel Orakwelu
[email protected]

School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Pietermaritzburg, South Africa | DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa.
Olumuyiwa Otegbeye
School of Computer Science and Applied Mathematics, Faculty of Science, University of the Witwatersrand, Johannesburg, South Africa
Hermane Mambili-Mamboundou
School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Pietermaritzburg, South Africa

Keywords:

Third-order, Hybrid block method, Convergence, Initial and boundary value problems

Abstract

This study presents a class of single-step, self-starting hybrid block methods for directly solving general third-order ordinary differential equations (ODEs) without reduction to first order equations. The methods are developed through interpolation and collocation at systematically selected evenly spaced nodes with the aim of boosting the accuracy of the methods. The zero stability, consistency and convergence of the algorithms are established. Scalar and systems of linear and nonlinear ODEs are approximated to test the effectiveness of the schemes, and the results obtained are compared against other methods from the literature. Significantly, the study shows that an increase in the number of intra-step points improves the accuracy of the solutions obtained using the proposed methods.

Dimensions

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