List of top Engineering Mathematics Questions on Solutions of linear and non-linear algebraic equations

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

\(\frac{P}{Q}\) is not equal 1, \(\left(\frac{P}{Q}\right)^{\frac{P}{Q}} = P^{\frac{P}{Q} - 1}\)