In order to numerically solve the ordinary differential equation 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 $n = 0, 1, 2, \ldots.$ This numerical scheme will yield a solution with non-physical oscillations for $\Delta t > h.$ The value of h is

Consider the definite integral

$\int^2_1(4x^2+2x+6)dx$

Let I_e be the exact value of the integral. If the same integral is estimated using Simpson’s rule with 10 equal subintervals, the value is I_s. The percentage error is defined as e = 100 × (I_e - I_s)/I_e The value of e is