Simpson's method, error estimate

[Kqwert]

Homework Statement

Hello,

using Simpson´s method, one can calculate the number of intervals needed to achieve a given accuracy, through the error formula. Is there any other way to know that the required accuracy is achieved other than computing the integral and comparing it to the result from Simpson's method?

 

[DaveE]

Homework Statement

Is there any other way to know that the required accuracy is achieved other than computing the integral

No, not unless you have some additional constraints on what sort of function you are integrating. Think about some "pathological" (but still integral) functions that change values "unexpectedly".

 

[Ray Vickson]

Homework Statement

Hello,

using Simpson´s method, one can calculate the number of intervals needed to achieve a given accuracy, through the error formula. Is there any other way to know that the required accuracy is achieved other than computing the integral and comparing it to the result from Simpson's method?

That is not how error estimates are used in practice. Unless we know the exact value of the integral, we cannot know the exact error. However, there is a formula for an upper bound on the absolute value of the error (in terms of some bounds on the derivatives, etc.) The point is that the exact error formula contains some quantities that we do not know how to calculate exactly (in general), but if we work at it a bit we may be able so say that the error cannot exceed $***$. The exact error may be a lot less than $***$, buy we really have no easy way to tell.