id: 06618966
dt: j
an: 2016e.00984
au: Yang, Yajun; Gordon, Sheldon P.
ti: Numerical integration: one step at a time.
so: PRIMUS, Probl. Resour. Issues Math. Undergrad. Stud. 26, No. 5, 371-392
(2016).
py: 2016
pu: Taylor \& Francis, Philadelphia, PA
la: EN
cc: N45 I55
ut: numerical integration; Riemann sums; trapezoidal rule; adaptive methods of
integration
ci:
li: doi:10.1080/10511970.2015.1127300
ab: Summary: This article looks at the effects that adding a single extra
subdivision has on the level of accuracy of some common numerical
integration routines. Instead of automatically doubling the number of
subdivisions for a numerical integration rule, we investigate what
happens with a systematic method of judiciously selecting one extra
subdivision for the succeeding iteration. We outline the numerical
criterion for both Riemann sums and the Trapezoidal Rule, respectively.
Two kinds of integrands where this technique is very effective are
considered: as a computational tool and more importantly as a way to
increase student understanding.
rv: