Summary
The numerical error of standard finite-difference schemes is analyzed at free boundaries of the Grad-Schlüter-Shafranov equation of plasma physics. A simple correction strategy is devised to eliminate (to leading order) the errors which arise as the free boundary crosses the rectangular grid at irregular locations. The resulting scheme can be solved by Gauss-Newton or Inverse iterations, or by multigrid iterations. Extrapolation (from 2nd to 3rd order of accuracy) is possible for the new scheme.
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Dedicated to the memory of Professor Lothar Collatz
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Meyer-Spasche, R., Fornberg, B. Discretization errors at free boundaries of the Grad-Schlüter-Shafranov equation. Numer. Math. 59, 683–710 (1991). https://doi.org/10.1007/BF01385804
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DOI: https://doi.org/10.1007/BF01385804