Euler scheme
For the differential equation depending on time $$ \begin{equation} \frac{dT}{dt} = f(t,T) \end{equation} $$ subject to the initial condition $$ \begin{equation} T = \alpha\quad\text{for}\quad t = 0. \end{equation} $$ Euler scheme can be expressed by: $$ \begin{equation} w_{k+1} = w_k + h f(t_k,w_k)\quad{with}\quad w_0 = \alpha. \end{equation} $$