Boundary stability is a mesh-uniform estimate for a finite-difference initial-boundary problem with forced boundary data. Stability of the whole-line Cauchy scheme is necessary but may fail to control boundary-supported numerical modes.
After transforming time and tangential variables, the uniform Kreiss--Lopatinskii condition requires the boundary equations to determine every decaying normal mode with an inverse bounded uniformly over transformed frequencies. It rules out growing or weakly controlled boundary modes.

Ancestors (7)

  1. Von Neumann stability analysis
  2. Finite difference method
  3. Numerical analysis
  4. Analysis
  5. Area of mathematics
  6. Mathematics
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