Abstract
A comparative study is undertaken of 5- and 9-point discretizations of the linear source problem on a rectangular mesh, and of 3-point discretizations of its one-dimensional analogue. Traditional difference and (Richardson) extrapolation methods compare very favorably with variational methods. Sample result : Courant’s derivation of, the standard 5-point formula for the Laplace equation from the Ritz variational method does not generalize to the Poisson or Helmholtz equation.
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