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 varia- tional 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. 1. Introduction. We make below a comparative study of 5-point and 9-point discretizations of the differential equation of the linear source problem, (1) -V * (pVu) + qu = f, p(x, y) > O, q _ O, for piecewise smooth p, q and f on a rectangular mesh. We also study 3-point approximations to its one-dimensional analogue:
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