logistic¶
- 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 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.
- Parameters
t0 – Initial time.
tmax – Final time.
y0 – (shape=(1, )) – Initial value. Default is
[0.1].params – Parameters \((a, b)\) of the logistic IVP.
- Returns
InitialValueProblem object describing the logistic ODE with the prescribed configuration.
- Return type