I have a quantity [itex]U(x)[/itex], x>0, which I cannot calculate exactly. Numerically, I can calculate an approximation [itex]u(x;\eta)[/itex], for [itex]\eta>0[/itex], which is very close to [itex]U(x)[/itex] if [itex]\eta[/itex] is small enough. I know that the error [itex]\xi(x;\eta)=u(x;\eta)-U(x)[/itex] satisfies an estimate(adsbygoogle = window.adsbygoogle || []).push({});

[tex]|\xi(x;\eta)|\le E(x;\eta)[/tex]

where [itex]\lim_{\eta\to 0}E(x;\eta)=0[/itex] for all x, and I can use this to choose my parameter [itex]\eta[/itex] so that the error lies under a specified tolerance.

Based only on the above, is it possible to derive an approximate estimate for the error in [itex]\partial_x u(x;\eta)[/itex], i.e. [itex]\partial_x \xi(x;\eta)[/itex]?

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# Error estimate

Can you offer guidance or do you also need help?

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