Truncation Error

Updated 15 Sep 2026

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What it is
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  the error introduced by stopping a Taylor series (or any infinite process) at a finite order $n$ , rather than a rounding/representation error
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Order of convergance
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  each additional order added to the series typically reduces the error by roughly a factor of $h$ (the step size) — e.g. approximating $\ln(1.1)$ with $x=0.1$ , each added order improves accuracy by about 10×
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Related
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  Taylor Series
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  Numerical Differentiation

Linked references 2