Basic Principle of the Verification

  • Mitsuhiro T. Nakao
  • Michael Plum
  • Yoshitaka Watanabe
Part of the Springer Series in Computational Mathematics book series (SSCM, volume 53)


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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Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Mitsuhiro T. Nakao
    • 1
  • Michael Plum
    • 2
  • Yoshitaka Watanabe
    • 3
  1. 1.Faculty of MathematicsKyushu UniversityFukuokaJapan
  2. 2.Faculty of MathematicsKarlsruhe Institute of TechnologyKarlsruheGermany
  3. 3.Research Institute for Information TechnologyKyushu UniversityFukuokaJapan

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