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

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  • Saidu Daudu Yakubu
  • Precious Sibanda
  • Saeid Abbasbandy

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.

Suggested Citation

  • Saidu Daudu Yakubu & Precious Sibanda & Saeid Abbasbandy, 2024. "One-Step Family of Three Optimized Second-Derivative Hybrid Block Methods for Solving First-Order Stiff Problems," Journal of Applied Mathematics, Hindawi, vol. 2024, pages 1-18, April.
    • Handle: RePEc:hin:jnljam:5078943
    DOI: 10.1155/2024/5078943
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