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Finite-difference stability

MediumFinance & DerivativesProgramming & DSA~4m

An explicit finite-difference scheme for a parabolic PDE is stable only if Δt/(Δx)2≤12\Delta t/(\Delta x)^2 \le \tfrac12. To keep it stable, which is worse to have too many of?

Show hints (2)+
  1. The stability ratio has (Δx)2(\Delta x)^2 in the denominator.
  2. Smaller Δx\Delta x makes the ratio explode.

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