# 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. 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) Interface for ODESolver. GaussianIVPFilter(ivp, gaussfilt, with_smoothing) ODE solver that behaves like a Gaussian filter. ODEPrior(driftmat, dispmat, ordint, spatialdim) Prior dynamic model for ODE filtering and smoothing. IBM(ordint, spatialdim, diffconst[, …]) Integrated Brownian motion of order $$q$$ prior. IOUP(ordint, spatialdim, driftspeed, diffconst) IOUP(q) prior: Matern(ordint, spatialdim, lengthscale, …) Matern(q) prior –> Matern process with reg. (Adaptive) step size rules for ODE solvers. ConstantSteps(stepsize) Constant step size rule for ODE solvers. AdaptiveSteps(tol_per_step, localconvrate[, …]) Adaptive step size selection based on tolerance per step. ODESolution(times, rvs, solver) Gaussian IVP filtering solution of an ODE problem.