# L-Stable Block Hybrid Numerical Algorithm for First-Order Ordinary Differential Equations

• B. I. Akinnukawe Department of Mathematics, University of Lagos, Lagos, Nigeria
• K. O. Muka Department of Mathematics, University of Benin, Benin city, Nigeria
Keywords: Second derivative, Stability, Hybrid, Block, Collocation techniques

### Abstract

In this work, a one-step L-stable Block Hybrid Multistep Method (BHMM) of order five was developed. The method is constructed for solving first order Ordinary Differential Equations with given initial conditions. Interpolation and collocation techniques, with power series as a basis function, are employed for the derivation of the continuous form of the hybrid methods. The discrete scheme and its second derivative are derived by evaluating at the specific grid and off-grid points to form the main and additional methods respectively. Both hybrid methods generated are composed in matrix form and implemented as a block method. The stability and convergence properties of BHMM are discussed and presented. The numerical results of BHMM have proven its efficiency when compared to some existing methods.

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Published
2020-08-01
How to Cite
Akinnukawe, B. I., & Muka, K. O. (2020). L-Stable Block Hybrid Numerical Algorithm for First-Order Ordinary Differential Equations. Journal of the Nigerian Society of Physical Sciences, 2(3), 160-165. https://doi.org/10.46481/jnsps.2020.108
Section
Original Research