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.

Newton(;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.