Numerical verification methods for solutions of semilinear elliptic boundary value problems

@article{Nakao2011NumericalVM,
  title={Numerical verification methods for solutions of semilinear elliptic boundary value problems},
  author={Mitsuhiro T. Nakao and Yoshitaka Watanabe},
  journal={Nonlinear Theory and Its Applications, IEICE},
  year={2011},
  volume={2},
  pages={2-31}
}
This article describes a survey on numerical verification methods for second-order semilinear elliptic boundary value problems introduced by authors and their colleagues. Here “numerical verification” means a computer-assisted numerical method for proving the existence of a solution in a close and explicit neighborhood of an approximate solution. Three kinds of methods based on the infinite dimensional fixed-point theorems using Newton-like operator will be presented. In each verification… 

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