A student is approximating the solution to a differential equation by successively…
MATHEMATICS · Single correct · AP · Calculus BC · Differential Equations · Differential Equations
Problem
A student is approximating the solution to a differential equation by successively updating (x,y) pairs with a fixed increment Δx. If Δx is halved while all other aspects of the procedure remain the same, which of the following best describes the most likely effect on the numerical approximation at a given point?
(a) The absolute error will be approximately cut to one-quarter of its previous size.
(b) The absolute error will double because twice as many steps are required.
(c) The absolute error will be approximately cut in half.
(d) The absolute error will remain essentially unchanged.