ODE

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 (y_{n+1} - y_n) / Δt = -...

The ordinary differential equation $\frac{dy}{dt} = -\pi y$ subject to an initial condition $y(0) = 1$ is solved numerically using the following scheme: $\frac{y(t_{n+1}) - y(t_n)}...

The differential equation \frac{d^2y}{dx^2} + 16y = 0 for y(x) with the two boundary conditions \frac{dy}{dx}|_{x=0} = 1 and \frac{dy}{dx}|_{x=\frac{\pi}{2}} = -1 has