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ODE and PDE Stability Analysis

Stability of ODE vs Stability of Method • Stability of ODE solution: Perturbations of solution do not diverge away over time • Stability of a method: – Stable if small perturbations do not cause the solution to diverge from each other without bound – Equivalently: Requires that solution at any fixed time t remain bounded as h → 0 (i.e., # steps to get to t grows)

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