Numerical solutions of ordinary differential equations using Spline-Integral Operator
<|reference_start|>Numerical solutions of ordinary differential equations using Spline-Integral Operator: In this work, we introduce a novel numerical method for solving initial value problems associated with a given differential. Our approach utilizes a spline approximation of the theoretical solution alongside the integral formulation of the analytical solution. Furthermore, we offer a rigorous proof of the method's order and provide a comprehensive stability analysis. Additionally, we showcase the effectiveness method through some examples, comparing with Taylor's methods of same order.<|reference_end|>
@article{salgado2024numerical,
    title={Numerical solutions of ordinary differential equations using
  Spline-Integral Operator},
    author={Gustavo H. O. Salgado and Jo~ao P. R. Romanelli},
    journal={arXiv preprint arXiv:2409.20369},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.20369},
    primaryClass={math.NA cs.NA}
}