Question: For trapezoid and Simpson methods, the numerical integration have relative error where is the numerical result using intervals between [0, 1]. (i) Explain the power-law

For trapezoid and Simpson methods, the numerical integration have relative error is the numerical result using intervals between [0, 1]. (i) Explain the

where power-law scaling with an exponent 1.5 (instead of 2 and 4 as is the numerical result using expected for the trapezoid and Simpson's method, respectively). (ii) How can one intervals between [0, 1].

(i) Explain the power-law scaling with an exponent 1.5 (instead of 2 and 4 as expected for the trapezoid and Simpson's method, respectively).

(ii) How can one circumvent this problem and restore the desired error scaling ?

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