One-Step Family of Three Optimized Second-Derivative Hybrid Block Methods for Solving First-Order Stiff Problems

Saidu Daudu Yakubu, Precious Sibanda and Saeid Abbasbandy

Journal of Applied Mathematics, 2024, vol. 2024, 1-18

Abstract: This paper introduces a novel approach for solving first-order stiff initial value problems through the development of a one-step family of three optimized second-derivative hybrid block methods. The optimization process was integrated into the derivation of the methods to achieve maximal accuracy. Through a rigorous analysis, it was determined that the methods exhibit properties of consistency, zero-stability, convergence, and A-stability. The proposed methods were implemented using the waveform relaxation technique, and the computed results demonstrated the superiority of these schemes over certain existing methods investigated in the study.

Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:5078943

DOI: 10.1155/2024/5078943

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