An Efficient Approach to the Numerical Verification for Solutions of Elliptic Differential Equations

@article{Nakao2004AnEA,
  title={An Efficient Approach to the Numerical Verification for Solutions of Elliptic Differential Equations},
  author={Mitsuhiro T. Nakao and Yoshitaka Watanabe},
  journal={Numerical Algorithms},
  year={2004},
  volume={37},
  pages={311-323}
}
The authors and their colleagues have developed numerical verification methods for solutions of second-order elliptic boundary value problems based on the infinite-dimensional fixed-point theorem using the Newton-like operator with appropriate approximation and constructive a priori error estimates for Poisson's equations. Many verification results show that the authors' methods are sufficiently useful when the equation has no first-order derivative. However, in the case that the equation… CONTINUE READING