Single Step Block Linear Approach for Solving Initial Value Problems Second Order Ordinary Differential Equation

Ayinde Muhammed Abdullahi, University of Abuja, Gwagwalada, Abuja, NIGERIA, Abuja, FCT, AbujaFollow
John Sabo, Adamawa State University, Mubi, Nigeria
Taiye Oyedepo, Federal College of Dental Technology and Therapy, Enugu, Nigeria
Chukkol Buba Yusuf, Modibbo Adama University, Yola, Nigeria
Salihu Ibrahim, University of Abuja, Abuja, Nigeria

Document Type

Original Study

Abstract

The analysis of single step block hybrid method using the linear block approach for solving second order oscillatory initial value problems of ordinary differential equation is developed in this paper. The numerical properties of this block method are established, demonstrating its consistency, convergence, and zero-stability. To demonstrate the superiority of the block method, it was tested on three mathematical problems involving second-order initial value problems. The results obtained from these tests outperformed the existing approaches found in literature, showcasing the enhanced performance and accuracy of the proposed block method.

Keywords

Block hybrid method; Consistency; convergence; zero-stability; Numerical Properties; Single-step

Recommended Citation

Abdullahi, Ayinde Muhammed; Sabo, John; Oyedepo, Taiye; Yusuf, Chukkol Buba; and Ibrahim, Salihu (2024) "Single Step Block Linear Approach for Solving Initial Value Problems Second Order Ordinary Differential Equation," Al-Qadisiyah Journal of Pure Science: Vol. 30 : No. 1 , Article 1.
Available at: https://doi.org/10.29350/2411-3514.1229