Adaptive Time-Step Semi-Implicit One-Step Taylor Scheme for Stiff Ordinary Differential Equations
<|reference_start|>Adaptive Time-Step Semi-Implicit One-Step Taylor Scheme for Stiff Ordinary Differential Equations: In this study, we propose high-order implicit and semi-implicit schemes for solving ordinary differential equations (ODEs) based on Taylor series expansion. These methods are designed to handle stiff and non-stiff components within a unified framework, ensuring stability and accuracy. The schemes are derived and analyzed for their consistency and stability properties, showcasing their effectiveness in practical computational scenarios.<|reference_end|>
@article{boscarino2024adaptive,
    title={Adaptive Time-Step Semi-Implicit One-Step Taylor Scheme for Stiff
  Ordinary Differential Equations},
    author={S. Boscarino and E. Macca},
    journal={arXiv preprint arXiv:2409.11990},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.11990},
    primaryClass={math.NA cs.NA}
}