## A Framework for the Numerical Computation and A Posteriori Verification of Invariant Objects of Evolution Equations

- Jordi-Lluís Figueras, Marcio Gameiro, Jean-Philippe Lessard, Rafael de la Llave
- SIAM J. Applied Dynamical Systems
- 2017

@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} }

- Published 2004 in Numerical Algorithms
DOI:10.1023/B:NUMA.0000049477.75366.94

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

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