Development of a block method for solving multiple order ODEs

Emmanuel Oluseye Adeyefa, Adewale Adeyemi James, Adeyemi Sunday Olagunju and Folake Lois Joseph

International Journal of Mathematics in Operational Research, 2024, vol. 29, issue 1, 51-65

Abstract: In this work, a convergent hybrid block method (CHBM) with two off-grid points for direct integration of first, second, and third-order initial value problems (IVPs) is proposed. The development of a block method for the solution of IVPs has been considered overwhelmingly in the literature. However, using a block method to directly solve multi-order IVPs has not been so common. Thus, the formulation of a single numerical algorithm for the direct numerical integration of first, second and third-order IVPs is our focus. The method is formulated from a continuous scheme derived using collocation and interpolation techniques and implemented in a block-by-block manner as a numerical integrator for IVPs. To assess the method's applicability, efficiency, and accuracy, the convergence analysis has been investigated, and six test problems are considered.

Keywords: block method; collocation; convergence; interpolation; multiple order ODEs. (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:ids:ijmore:v:29:y:2024:i:1:p:51-65

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