Integreat`RK`
Integreat`RK`

RK

RK[]

returns a Dataset containing a catalog of Runge–Kutta methods.

RK["name"]

retrieves the method named name from the catalog.

RK[s]

constructs a generic s-stage Runge–Kutta method.

RK[A,b,c]

constructs a Runge–Kutta method with coefficients A, b, and c.

RK[A,b]

constructs a Runge–Kutta method with c coefficients that are the row sum of A.

RK[A]

constructs a stiffly accurate Runge–Kutta method.

RK[A,b,c,bHat]

constructs an embedded Runge–Kutta pair.

RK[rk,bHat]

adds embedded coefficients bHat to rk.

Details and Options

  • An stage Runge–Kutta method is given by , with stages , for .
  • An RK object represent a Runge–Kutta method optionally including an embedded method.
  • RK[…] displays in a notebook as a Butcher tableau.
  • Dense output is supported by specifying b coefficients which depend on θ.

Examples

Basic Examples  (4)

Create a generic three stage Runge–Kutta methods:

Create the backward Euler method:

Load the classical fourth order Runge–Kutta method from the catalog:

Create an embedded pair with dense output:

Tech Notes
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  • Runge–Kutta Methods