Solving Ode With Python Reversely

In Python we solve a differential equation OD_H with an initial point y0 = od0 in a specific point z similar to the following code def OD_H(od, z, c, b): .... return .... od

Solution 1:

In this case, you are proposing a root problem where the solver function evaluated minus the desired answer is the function f(x) where f(x)=0.
Because ODE solver returns point arrays and not callable functions, you need to interpolate first the solution points. Then, this is used in root finding problem.

from scipy.integrate import solve_ivp # Recommended initival value problem solver
from scipy.interpolate import interp1d # 1D interpolation
from scipy.optimize import brentq # Root finding method in an interval
exponential_decay = lambda t, y: -0.5 * y # dy/dt = f(t, y)
t_span = [0, 10] # Interval of integration
y0 = [2] # Initial state: y(t=t_span[0])=2
desired_answer = 0.59
sol_ode = solve_ivp(exponential_decay, t_span, y0) # IVP solution
f_sol_ode = interp1d(sol_ode.t, sol_ode.y) # Build interpolated function
brentq(lambda x: f_sol_ode(x) - desired_answer, t_span[0], t_span[1])