The numerical solution of some elliptic boundary value problems by integral operator methods

  • R. P. Gilbert
  • Peter Linz
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 430)


An integral representation for the solution of elliptic equations of the form Δnu - P(r2)u=0, developed by Gilbert, is used to construct approximate solutions for problems of this type. Properties of the G-function, needed in the integral representation, are discussed and a numerical scheme for its computation is given. The approximate G-function is used to represent the solution and minimization techniques are used to satisfy the boundary conditions. A discussion of the practical usefulness of methods of this type is given.


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Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • R. P. Gilbert
    • 1
  • Peter Linz
    • 2
  1. 1.Department of MathematicsIndiana UniversityUSA
  2. 2.Department of MathematicsUniversity of California at DavisUSA

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