In this paper, an efficient numerical solver based on a hybrid optimized block method is constructed and analyzed for approximating solutions of first-order initial value problems. The scheme is designed in such a way that each block contains three steps with three off-step points. To enhance its efficiency, we introduce simplified formulations of the underlying equations and employ an adaptive step-size strategy based on local error estimates. We establish the stability region, the order of consistency, and the convergence properties of the method. The effectiveness of the proposed approach is demonstrated through its application to several test problems.
Aderogba, A. Abiodun and Ramos, H. (2026). Adaptive stepsize optimized three-step hybrid block method for first-order initial value problems. Computational Methods for Differential Equations, (), -. doi: 10.22034/cmde.2025.67304.3197
MLA
Aderogba, A. Abiodun, and Ramos, H. . "Adaptive stepsize optimized three-step hybrid block method for first-order initial value problems", Computational Methods for Differential Equations, , , 2026, -. doi: 10.22034/cmde.2025.67304.3197
HARVARD
Aderogba, A. Abiodun, Ramos, H. (2026). 'Adaptive stepsize optimized three-step hybrid block method for first-order initial value problems', Computational Methods for Differential Equations, (), pp. -. doi: 10.22034/cmde.2025.67304.3197
CHICAGO
A. Abiodun Aderogba and H. Ramos, "Adaptive stepsize optimized three-step hybrid block method for first-order initial value problems," Computational Methods for Differential Equations, (2026): -, doi: 10.22034/cmde.2025.67304.3197
VANCOUVER
Aderogba, A. Abiodun, Ramos, H. Adaptive stepsize optimized three-step hybrid block method for first-order initial value problems. Computational Methods for Differential Equations, 2026; (): -. doi: 10.22034/cmde.2025.67304.3197
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