Integreat`GLM`
Integreat`GLM`

GLM

GLM[s,r,p]

constructs a generic general linear method with s internal stages and r external stages which are expanded to order p.

GLM[A,B,U,V,Q,c]

constructs a general linear method with coefficients , , , , , and .

GLM[rk]

converts a Runge–Kutta method rk into a general linear method.

GLM[rk,p]

converts a Runge-Kutta method rk into a general linear method with external stages expanded to order p.

GLM[lmm]

converts a linear multistep method lmm into a general linear method.

Details and Options

  • A general linear method with internal stages and external stages is given by , for , and , for . The external stages have the Taylor series expansion , for .
  • A GLM object represents a general linear method.
  • GLM[…] displays in a notebook as a Butcher tableau.

Examples

Basic Examples  (3)

Create a generic general linear method with two internal stages and three internal stages:

Construct a general linear method from coefficients:

Convert the classical fourth order Runge–Kutta method into a general linear method:

Convert the three-step Adams–Moulton method into a general linear method:

Tech Notes
▪
  • General Linear Methods