probnum.problems.zoo.diffeq.logistic(t0=0.0, tmax=2.0, y0=None, params=(3.0, 1.0))[source]

Initial value problem (IVP) based on the logistic ODE.

The logistic ODE is defined through

\[f(t, y) = a y \left( 1 - \frac{y}{b} \right)\]

for some parameters \((a, b)\). Default is \((a, b)=(3.0, 1.0)\). This implementation includes the Jacobian \(J_f\) of \(f\) as well as a closed form solution given by

\[f(t) = \frac{b y_0 \exp(a t)}{b + y_0 \left[ \exp(at) - 1 \right]}\]

where \(y_0= y(t_0)\) is the initial value.

  • t0 – Initial time. Default is 0.0

  • tmax – Final time. Default is 2.0

  • y0(shape=(1, )) – Initial value. Default is [0.1].

  • params – Parameters \((a, b)\) for the logistic IVP. Default is \((a, b) = (3.0, 1.0)\).


InitialValueProblem object describing the logistic ODE with the prescribed configuration.

Return type