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

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.