10. Solving the differential equation

We'll solve the equation exactly, and after explaining the Crank-Nicolson scheme, we'll give an approximate solution. We want to perform a calculation between time t - 1 and time t of the simulation. This involves solving the differential equation between 0 and 1, taking ${\theta }_{\text{m}}\left(0\right)={\theta }_{\text{m}}^{\text{t}-1}$ as the initial condition.

• Direct resolution

  We want to perform a calculation between time t - 1 and time t of the simulation. This involves solving the differential equation between 0 and 1, taking ${\theta }_{\text{m}}\left(0\right)={\theta }_{\text{m}}^{\text{t}-1}$...