Implicit one-step optimized fourth-derivative hybrid block method for directly solving general third-order IVPs

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This paper introduces a single-step optimized fourth-derivative block hybrid method specifically designed to solve general third-order initial value problems directly. By incorporating advanced optimization techniques, the method significantly improves accuracy and computational efficiency. Extensive analysis confirms that the method exhibits zero-stability, consistency, A-stability, and convergence properties. Numerical experiments conducted in this study reveal that the proposed method surpasses existing approaches in accuracy, establishing it as a significant advancement in the numerical solution of higher-order initial value problems.

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