Streamlined Approach to Intra-Step Second Derivative Block in Stiff Initial Value Problem Systems

One of the distinctive attributes of the proposed techniques is their inherent self-starting nature, enabling their application as concurrent numerical integrators on distinct non-overlapping intervals. To demonstrate the efficacy of the advanced algorithms, their application extends to the realm of stiff systems of initial value problems (IVPs). The attained results are then subjected to a comparative analysis against outcomes derived from relevant schemes and alternative methodologies available in the existing body of literature.

The presented approach represents a significant stride towards refining the precision and reliability of numerical solutions for ODEs. The augmentation of intra-step points, achieved through the innovative modification of existing algorithms, not only heightens accuracy but also strengthens the algorithms’ convergence properties. The application of power series polynomial interpolation in tandem with Bhaskara cosine formula-generated intra points showcases the ingenuity of this approach. The adaptability of the proposed algorithms to non-overlapping intervals adds to their practicality and widens their scope of application. Through rigorous comparison with established techniques, the superior performance of the proposed algorithms is substantiated, further solidifying their potential to address complex problems in various domains.

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