A Boundary-Domain Integral Equation Method for an Elliptic Cauchy Problem with Variable Coefficients

  • Andriy Beshley
  • Roman Chapko
  • B. Tomas JohanssonEmail author
Conference paper
Part of the Trends in Mathematics book series (TM)


We consider an integral based method for numerically solving the Cauchy problem for second-order elliptic equations in divergence form with spacewise dependent coefficients. The solution is represented as a boundary-domain integral, with unknown densities to be identified. The given Cauchy data is matched to obtain a system of boundary-domain integral equations from which the densities can be constructed. For the numerical approximation, an efficient Nyström scheme in combination with Tikhonov regularization is presented for the boundary-domain integral equations, together with some numerical investigations.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Andriy Beshley
    • 1
  • Roman Chapko
    • 1
  • B. Tomas Johansson
    • 2
    Email author
  1. 1.Faculty of Applied Mathematics and InformaticsIvan Franko National University of LvivLvivUkraine
  2. 2.School of MathematicsAston UniversityBirminghamUK

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