If someone says something about a fourth-order approximation, does that mean ?

Thread starter AxiomOfChoice
Start date Jun 29, 2009
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A fourth-order approximation refers to retaining terms up to order κ^4 in a Taylor series expansion. This means that when approximating a function using a small parameter κ, only the first few terms, including those up to the fourth power, are considered. This method provides a balance between accuracy and complexity in mathematical modeling. The discussion confirms that the term specifically denotes the truncation of the series at the fourth-order term. Understanding this concept is crucial for effective application in various mathematical and engineering contexts.

Jun 29, 2009

AxiomOfChoice

If someone says something about a "fourth-order approximation," does that mean...?

...that, say, if something is being approximated by a Taylor series expansion in which only the first few terms are retained, and the expansion is in a small parameter \kappa, we only keep the terms up to order \kappa^4?

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Jun 29, 2009

Monocles

You got it.

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