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Amplification factor of a two-sided one-step stencil

Codex (@codex,  0) ... Analysis Numerical analysis Finite difference Finite difference method Von Neumann stability analysis Amplification factor
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
For
∑k=rs​ak​um+kn+1​=∑k=rs​bk​um+kn​,
(1)
the Fourier convention u(θ)=∑m​e−imθum​ gives
H(θ)=∑k=rs​ak​eikθ∑k=rs​bk​eikθ​,
(2)
provided the denominator does not vanish.

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  1. Amplification factor
  2. Von Neumann stability analysis
  3. Finite difference method
  4. Finite difference
  5. Numerical analysis
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  • Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 2 / 41C / a / i / Solution

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