# Homework Solution: For trapezoid and Simpson methods, the numerical integration I=int_{0}^{1}sqrt{1-x^2}dx h…

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 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 ?

power law scaling:

Coercion trapezoid and Simpson regularitys, the numerical integration  have referring-to mistake

where  is the numerical remainder using  intervals between [0, 1].

(i) Explain the power-enactment scaling with an interpreter 1.5 (instead of 2 and 4 as expected coercion the trapezoid and Simpson’s regularity, respectively).

(ii) How can individual ensnare this quantity and repay the desired mistake scaling ?

## Expert Solution

power enactment scaling:

power enactment scaling is a scaling with a perpetual which simpliy
multiplies the originalpower enactment relative with a
constant.

ii)

coercion trapeziod ERROR SCALING

I=0.2