Numerical verification methods for a system of elliptic PDEs, and their software library

@article{Sekine2021NumericalVM,
  title={Numerical verification methods for a system of elliptic PDEs, and their software library},
  author={Kouta Sekine and Mitsuhiro T. Nakao and Shin'ichi Oishi},
  journal={Nonlinear Theory and Its Applications, IEICE},
  year={2021}
}
Since the numerical verification method for solving boundary value problems for elliptic partial differential equations (PDEs) was first developed in 1988, many methods have been devised. In this paper, existing verification methods are reformulated using a convergence theorem for simplified Newton-like methods in the direct product space Vh×V⊥ of a computable finite-dimensional space Vh and its orthogonal complement space V⊥. Additionally, the Verified Computation for PDEs (VCP) library is… 
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