Computer-assisted proofs for semilinear elliptic boundary value problems

@article{Plum2009ComputerassistedPF,
  title={Computer-assisted proofs for semilinear elliptic boundary value problems},
  author={Michael Plum},
  journal={Japan Journal of Industrial and Applied Mathematics},
  year={2009},
  volume={26},
  pages={419-442}
}
  • M. Plum
  • Published 1 October 2009
  • Mathematics
  • Japan Journal of Industrial and Applied Mathematics
For second-order semilinear elliptic boundary value problems on bounded or unbounded domains, a general computer-assisted method for proving the existence of a solution in a “close” and explicit neighborhood of an approximate solution, computed by numerical means, is proposed. To achieve such an existence and enclosure result, we apply Banach’s fixed-point theorem to an equivalent problem for the error, i.e., the difference between exact and approximate solution. The verification of the… 

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