Accurate numerical solutions are sought for two dimensional boundary problems in which the function u(x, y) satisfies
$$\begin{array}{*{20}{c}} { - \Delta [u(x,y)] = g(x,y),}&{(x,y) \in \;\Omega }\\ {u(x,y) = f(x,y),}&{(x,y) \in \;\partial {\Omega _1}}\\ {\frac{{\partial u(x,y)}}{{\partial v}} = 0,}&{(x,y) \in \;\partial {\Omega _2}} \end{array}$$
where A is the Laplacian operator, Ω ⊂ E 2 is a simply connected open bounded domain with boundary ∂Ω = ∂Ω1 ⋃ ∂Ω2; ∂Ω2 may be empty; f, g are given functions: and \(\frac{\partial }{{\partial v}}\) is the derivative in the direction of the outward normal to the boundary.


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Copyright information

© Springer Basel AG 1974

Authors and Affiliations

  • R. E. Barnhill
    • 1
  • J. R. Whiteman
    • 2
  1. 1.Salt Lake CityUSA
  2. 2.UxbridgeUK

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