GPH - International Journal of Mathematics <p style="font-family: Aptos;"><strong><span style="color: #222222;"><span style="font-family: 'Aptos', serif;"><span style="aptos: Arial, serif;"><span style="font-size: medium; font-family: 'Aptos', serif;"><span style="color: #000000;">The</span></span></span><span style="aptos: Arial, serif;"><span style="font-size: medium; font-family: 'Aptos', serif;"><span style="color: #000000;"> GPH-INTERNATIONAL JOURNAL OF MATHEMATICS (E-ISSN 2795-3278 P-ISSN 2795-3274) </span></span></span><span style="helvetica: Arial, serif;"><span style="font-size: medium; font-family: 'Book Antiqua', serif;"><span style="color: #000000;">is an open-access journal that publishes research articles, reviews, case studies, guest-edited thematic issues, and short communications/letters in all areas of mathematics, applied mathematics, applied commutative algebra, and algebraic geometry, mathematical biology, physics and engineering, theoretical bioinformatics, experimental mathematics, etc</span></span></span></span></span>.<span style="font-size: medium;"> <a title="Journal Impact Factor" href=""><span style="color: #222222;"><span style="font-family: 'Book Antiqua', serif;"><span style="helvetica: Arial, serif;"><span style="color: #000000;"><span style="font-size: 1.5em;"><span style="text-shadow: #FF0000 0px 0px 2px;">Impact Factor: 1.114</span></span></span></span></span></span></a></span></strong></p> GLOBAL PUBLICATION HOUSE en-US GPH - International Journal of Mathematics <p>Author(s) and co-author(s)&nbsp;jointly&nbsp;and severally represent and warrant that the Article is original with the author(s) and does not infringe any&nbsp;copyright or violate any other right of any third parties, and that the Article has not been published&nbsp;elsewhere.&nbsp;Author(s) agree to the terms that the <strong>GPH Journal</strong> will have the full right to remove the published article on any misconduct found in the published article.</p> Development of Hybrid Block Integrator for the Numerical solution of Stiff and Oscillatory Differential Equations for first order Ordinary Differential Equations <p><strong>This paper discussed the development of a new numerical hybrid block integrator for the numerical solution of stiff and oscillatory differential equations for first order ordinary differential equations. The method of interpolation and collocation at some selected grid point to generate the continuous scheme was adopted. The research also investigates the consistency, convergence, zero-stability and region of absolute stability of the integrator using matlab and the integrator was tested on some numerical experiments for comparism. The analysis of the method showed that the method is Zero-stable, consistent, convergent and computationally stable. The method handles stiff and Oscillatory differential equations effectively.</strong></p> <p><strong>AMS Subject Classification: 65L05, 65L06, 65D30</strong></p> Abubakar Umaru Fotta Ahmad Abubakar Abubakar ##submission.copyrightStatement## 2024-01-13 2024-01-13 6 12 01 11 10.5281/zenodo.10522017