GATE Mechanical 2023 | Question: 40

Question

The initial value problem
$$
\frac{d y}{d t}+2 y=0, \quad y(0)=1
$$
is solved numerically using the forward Euler's method with a constant and positive time step of $\Delta t$.

Let $y_n$ represent the numerical solution obtained after $n$ steps. The condition $\left|y_{\mathrm{n}+1}\right| \leq\left|y_{\mathrm{n}}\right|$ is satisfied if and only if $\Delta t$ does not exceed _________.
 

(Answer in integer)