• Corpus ID: 203626652

A new formulation for the numerical proof of the existence of solutions to elliptic problems

@article{Sekine2019ANF,
  title={A new formulation for the numerical proof of the existence of solutions to elliptic problems},
  author={Kouta Sekine and Mitsuhiro T. Nakao and Shin'ichi Oishi},
  journal={ArXiv},
  year={2019},
  volume={abs/1910.00759}
}
Infinite-dimensional Newton methods can be effectively used to derive numerical proofs of the existence of solutions to partial differential equations (PDEs). In computer-assisted proofs of PDEs, the original problem is transformed into the infinite Newton-type fixed point equation $w = - {\mathcal L}^{-1} {\mathcal F}(\hat{u}) + {\mathcal L}^{-1} {\mathcal G}(w)$, where ${\mathcal L}$ is a linearized operator, ${\mathcal F}(\hat{u})$ is a residual, and ${\mathcal G}(w)$ is a local Lipschitz… 
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