# 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, …[, initrv]) 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. ODE Solution interface. KalmanODESolution(kalman_posterior) Gaussian IVP filtering solution of an ODE problem.