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Basic Principle of the Verification

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Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations

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Abstract

In this chapter, we describe the basic concept of our verification methods throughout Part I. The principle of our verification approaches was first originated in 1988 by one of the authors Nakao (Japan J Appl Math 5(2):313–332, 1988) for the second-order elliptic boundary value problems, and several improvements have since been made. This method consists of a projection and error estimations by the effective use of the compactness property of the relevant operator, and it can be represented in a rather generalized form in the examples below.

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Authors and Affiliations

  1. Faculty of Mathematics, Kyushu University, Fukuoka, Japan

    Mitsuhiro T. Nakao

  2. Faculty of Mathematics, Karlsruhe Institute of Technology, Karlsruhe, Germany

    Michael Plum

  3. Research Institute for Information Technology, Kyushu University, Fukuoka, Japan

    Yoshitaka Watanabe

Authors
  1. Mitsuhiro T. Nakao
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  2. Michael Plum
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  3. Yoshitaka Watanabe
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Nakao, M.T., Plum, M., Watanabe, Y. (2019). Basic Principle of the Verification. In: Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations. Springer Series in Computational Mathematics, vol 53. Springer, Singapore. https://doi.org/10.1007/978-981-13-7669-6_1

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