Student A uses a step size of and Student B uses a step size of to approximate the…
MATHEMATICS · Single correct · AP · Calculus BC · Differential Equations · Differential Equations
Problem
Student A uses a step size of 0.25 and Student B uses a step size of 0.10 to approximate the value of a solution to a first-order differential equation at the same point using a single-step numerical method. Which of the following statements best describes the absolute errors of their approximations at that point?
(a) Student A’s approximation will have the smaller absolute error because taking fewer steps limits the accumulation of rounding error.
(b) The absolute errors cannot be compared without first evaluating the exact integral of the differential equation over the interval.
(c) Student B’s approximation will have the smaller absolute error because a smaller step size reduces the accumulated truncation error.
(d) Student B’s approximation will have the larger absolute error because the increased number of steps causes the global error to accumulate.