domains / families / science / numerical-stability

numerical-stability

separate

Analyze and enforce numerical stability for time-dependent PDE simulations. Use when selecting time steps, choosing explicit/implicit schemes, diagnosing numerical blow-up, checking CFL/Fourier criteria, von Neumann analysis, matrix conditioning, or detecting stiffness in advection/diffusion/reaction problems.

When to use

• selecting time steps
• choosing explicit/implicit schemes
• diagnosing numerical blow-up
• checking CFL/Fourier criteria
• von Neumann analysis
• matrix conditioning
• detecting stiffness in advection/diffusion/reaction problems

When not to use

• **Explicit schemes only** for CFL/Fourier checks (implicit is unconditionally stable)
• **Von Neumann analysis** assumes linear, constant-coefficient, periodic BCs
• **Stiffness detection** requires eigenvalue estimates from user

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