- Cankaya University Journal of Science and Engineering
- Vol: 18 Issue: 1
- Hybrid Block Method for Direct Integration of First, Second and Third Order IVPs
Hybrid Block Method for Direct Integration of First, Second and Third Order IVPs
Authors : Adeyemi Olagunju, Emmanuel Adeyefa
Pages : 1-8
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Publication Date : 2021-05-01
Article Type : Research
Abstract :Construction of numerical methods for the solution of initial value problems (IVPs) in ordinary differential equations (ODEs) has been considered overwhelmingly in literature. However, the use of a single numerical method for the integration of ODEs of more than one order has not been commonly reported. In this paper, we focus on the development of a numerical method capable of obtaining the numerical solution of first, second and third-order IVPs. The method is formulated from continuous schemes obtained via collocation and interpolation techniques and applied in a block-by-block manner as a numerical integrator for first, second and third-order ODEs. The convergence properties of the method are discussed via zero-stability and consistency. Numerical examples are included and comparisons are made with existing methods in the literature.Keywords : Consistency, Convergence, Zero-Stability