MATHEMATICS · Single correct · AP · Calculus BC · Differential Equations · Differential Equations
Problem
A student notes that, when the step size in a numerical approximation of a solution curve is halved, the absolute error at the target point is consistently reduced from 0.044 to approximately 0.022. Which of the following statements best describes the relationship between step size and error suggested by these observations?
(a) The global error appears to be directly proportional to the square of the step size.
(b) The global error appears to be directly proportional to the step size.
(c) The global error appears to be inversely proportional to the step size.
(d) The global error appears to be independent of the step size.