Abstract
In this paper, we consider a numerical technique to verify the exact eigenvalues and eigenfunctions of second-order elliptic operators in some neighborhood of their approximations. This technique is based on Nakao’s method [9] using the Newton-like operator and the error estimates for the C∘ finite element solution. We construct, in computer, a set containing solutions which satisfies the hypothesis of Schauder’s fixed point theorem for compact map on a certain Sobolev space. Moreover, we propose a method to verify the eigenvalue which has the smallest absolute value. A numerical example is presented.
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Nakao, M.T., Yamamoto, N. & Nagatou, K. Numerical verifications for eigenvalues of second-order elliptic operators. Japan J. Indust. Appl. Math. 16, 307–320 (1999). https://doi.org/10.1007/BF03167360
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DOI: https://doi.org/10.1007/BF03167360