# 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. rigidbody(timespan, initrv) Initial value problem (IVP) for rigid body dynamics without external forces vanderpol(timespan, initrv[, params]) Initial value problem (IVP) based on the Van der Pol Oscillator. threebody(timespan, initrv[, params]) Initial value problem (IVP) based on a three-body problem. probsolve_ivp(ivp[, method, which_prior, …]) Solve initial value problem with Gaussian filtering and smoothing. ivp2ekf0(ivp, prior, evlvar) Computes measurement model and initial distribution for KF based on IVP and prior. ivp2ekf1(ivp, prior, evlvar) Computes measurement model and initial distribution for EKF based on IVP and prior. ivp2ukf(ivp, prior, evlvar) Computes measurement model and initial distribution for EKF based on IVP and prior.

## 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, gaussfilt, with_smoothing) ODE solver that behaves like 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(times, rvs, solver) Gaussian IVP filtering solution of an ODE problem.