About computation

For each Runge-Kutta method presented here, we propose some analysis. Each method is defined by its Butcher tableau:

Stability function

The stability function is the factor between two iterations when solve the Dahlquist equation with a Runge-Kutta method. It is defined as:

Stability domain

This is the set of each complex sush that amplification via the stability function is lower than 1 (no amplification):

Order star

Order star is defined in: as 3 sets:

Order

Count number of petals of the order star in a neighborhood of 0.

Stage order

The stage order is the highest integer sush:

Runge-Kutta method

To solve ODE with a Runge-Kutta method:

For an explicit method, there is no inversion of function, so we propose a short example of code.

Underlying Lawson method

To solve the ODE with the underlying Lawson method and solve exactly the linear part:

For an explicit method, there is no inversion of function, so we propose a short example of code.