Predictors and correctors

# Predictors and Correctors

We use a predictor-corrector scheme to track paths. These are the predictors and correctors currently available.

## Predictors

The following predictors are currently implemented.

``Euler()``

This uses the explicit Euler method for prediction, also known as the tangent predictor.

``Heun()``

The Heun predictor of order 2.

``Ralston()``

The Ralston predictor of order 2.

``RK3()``

The classical Runge-Kutta predictor of order 3.

``RK4()``

The classical Runge-Kutta predictor of order 4.

``Pade21()``

This uses a Padé-approximation of type (2,1) for prediction.

``NullPredictor()``

A predictor which does no prediction step, i.e., it just returns the input as its prediction.

## Correctors

The following correctors are currently implemented.

``NewtonCorrector(;simplified_last_step=true)``

An ordinary Newton's method. If `simplified_last_step` is `true`, then for the last iteration the previously Jacobian will be used. This uses an LU-factorization for square systems and a QR-factorization for overdetermined.