Abstract
This paper is a continuation of the preceding study ([2]) in which we described an automatic proof by computer, utilizing Schauder’s fixed point theorem, of the existence of weak solutions for Dirichlet problems of second order. We newly formulate a verification method using the Newton-like method and Sadovskii’s fixed point theorem for the codensing map. This approach enables us to remove the magnitude limit of the spectral radius of operator appeared in the previous work. We show some numerical examples which confirm us that the method is really applicable to problems having large spectral radius.
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Nakao, M.T. A numerical approach to the proof of existence of solutions for elliptic problems II. Japan J. Appl. Math. 7, 477–488 (1990). https://doi.org/10.1007/BF03167855
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DOI: https://doi.org/10.1007/BF03167855