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Counterexample

Is this true?

A convergent method is stable for any step size

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

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86 counterexamples are free — including most of the ones Part C leans on hardest.

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Numerical convergence

A scheme assumed to converge, or to converge at its advertised rate.

Drill statements like this
numericalstability

Go deeper· Explained in full in Numerical methods for ODE· Asked in CSIR NET June 2025· From Numerical Analysis › Numerical ODE: Euler, Runge–Kutta

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