# 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

InitialValueProblem