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math.NA2019★ 9 cited
A new formulation for the numerical proof of the existence of solutions to elliptic problems
Kouta Sekine, Mitsuhiro T. Nakao, Shin'ichi Oishi
Infinite-dimensional Newton methods can be effectively used to derive numerical proofs of the existence of solutions to partial differential equations (PDEs). In computer-assisted…
math.NA2019★ 1 cited
Inverse norm estimation of perturbed Laplace operators and corresponding eigenvalue problems
Kouta Sekine, Kazuaki Tanaka, Shin'ichi Oishi
In numerical existence proofs for solutions of the semi-linear elliptic system, evaluating the norm of the inverse of a perturbed Laplace operator plays an important role. We revea…