# probnum.diffeq¶

Differential Equations.

This package defines common dynamical models and probabilistic solvers for differential equations.

## Functions¶

 `logistic`(timespan, initrv[, params]) Initial value problem (IVP) based on the logistic ODE. `fitzhughnagumo`(timespan, initrv[, params]) Initial value problem (IVP) based on the FitzHugh-Nagumo model. `lotkavolterra`(timespan, initrv[, params]) Initial value problem (IVP) based on the Lotka-Volterra model. `seir`(timespan, initrv[, params]) Initial value problem (IVP) based on the SEIR model. `lorenz`(timespan, initrv[, params]) Initial value problem (IVP) based on the Lorenz system. `probsolve_ivp`(f, t0, tmax, y0[, df, method, …]) Solve initial value problem with Gaussian filtering and smoothing. Propose a suitable first step that can be taken by an ODE solver. `initialize_odefilter_with_rk`(f, y0, t0, …) Initialize an ODE filter by fitting the prior process to a few steps of an approximate ODE solution computed with Scipy’s RK. Initialize an ODE filter with Taylor-mode automatic differentiation.

## Classes¶

 `ODE`(timespan, rhs[, jac, hess, sol]) Ordinary differential equations. `IVP`(timespan, initrv, rhs[, jac, hess, sol]) Initial value problems (IVP). `ODESolver`(ivp, order) Interface for ODESolver. `GaussianIVPFilter`(ivp, prior_process, …[, …]) ODE solver that uses a Gaussian filter. `StepRule`(firststep) (Adaptive) step size rules for ODE solvers. `ConstantSteps`(stepsize) Constant step size rule for ODE solvers. `AdaptiveSteps`(firststep, atol, rtol[, …]) Adaptive step size selection using proportional control. `ODESolution`(locations, states[, derivatives]) ODE solution. `KalmanODESolution`(kalman_posterior) Gaussian IVP filtering solution of an ODE problem.