Simulation of Stiff Ordinary Differential Equations via a Simpson Third-Derivative Hybrid-Block Integrator.

Kaze Atsi; Geoffrey Micah Kumleng; Nathaniel Kamoh

doi:10.52589/AJMSS-IS1PJAC7

Simulation of Stiff Ordinary Differential Equations via a Simpson Third-Derivative Hybrid-Block Integrator. | AB Journals

Simulation of Stiff Ordinary Differential Equations via a Simpson Third-Derivative Hybrid-Block Integrator.

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African Journal of Mathematics and Statistics Studies

Vol. 9Issue 22026pp. 122–135Published 12 July 2026

DOI 10.52589/AJMSS-IS1PJAC7

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Abstract:

In this study, a Simpson's third derivative method is presented in hybrid-block form for the numerical simulation of stiff systems of ordinary differential equations. A multistep collocation approach has been adopted for the design of the new method. The new hybrid-block method is of order nine and has been examined to be consistent, zero-stable, convergent, and A(α)-stable. These findings are supported by numerical tests on stiff problems. The results of this study are compared with exact solutions and other existing methods.

Keywords:Stiff Ordinary Differential Equations Simpson’s Third Derivative Method Hybrid-Block Method Stability properties.

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