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Engineering Mathematics Question on Solutions of linear and non-linear algebraic equations

In order to numerically solve the ordinary differential equation dydt=−y\frac{dy}{dt}=-y for t > 0, with an initial condition y(0) = 1, the following scheme is employed
yn+1−ynΔt=12(yn+1+yn).\frac{y_{n+1}-y_n}{\Delta t}=\frac{1}{2}(y_{n+1}+y_n).
Here, Δ\Deltat is the time step and yn=y(nΔt)y_n = y(n\Delta t) for n = 0, 1, 2,…. This numerical scheme will yield a solution with non-physical oscillations for Δt>h\Delta t \gt h. The value of h is

A

12\frac{1}{2}

B

1

C

32\frac{3}{2}

D

2

Answer

2

Explanation

Solution

The correct option is (D): 4