Development of a block method for solving multiple order ODEs
by Emmanuel Oluseye Adeyefa; Adewale Adeyemi James; Adeyemi Sunday Olagunju; Folake Lois Joseph
International Journal of Mathematics in Operational Research (IJMOR), Vol. 29, No. 1, 2024

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.

Online publication date: Mon, 16-Sep-2024

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