Question

In order to numerically solve the ordinary differential equation \(\frac{dy}{dt}=-y\) for t > 0, with an initial condition y(0) = 1, the following scheme is employed
\(\frac{y_{n+1}-y_n}{\Delta t}=\frac{1}{2}(y_{n+1}+y_n).\)
Here, \(\Delta\)t is the time step and \(y_n = y(n\Delta t)\) for n = 0, 1, 2,…. This numerical scheme will yield a solution with non-physical oscillations for \(\Delta t \gt h\). The value of h is

• A. \(\frac{1}{2}\)
• B. 1
• C. \(\frac{3}{2}\)
• D. 2

Answer 1

The Correct Option is D

The correct option is (D): 4