Integreat Package

DocumentationInstallation
Examples
✖
https://wolfram.com/xid/0e2hzx1mgvi2drt4mimzyqq6
Integreat is a comprehensive Mathematica package for deriving and analyzing time integration methods including
  • Runge–Kutta (RK) methods
  • Functions for 30+ method properties
  • Support for embedded pairs and dense output
  • Order conditions generated via B-trees
  • Linear multistep methods (LMMs)
  • Constructors for Adams methods, BDF, Nyström methods, and other popular families
  • Functions for 10+ method properties
  • General linear methods (GLMs)
  • Functions for 15+ method properties
  • Support for casting RK methods and LMMs as GLMs
  • Order conditions for high stage order methods
  • Trees for Taylor series analysis
  • B-trees
  • N-trees for partitioned ODEs
  • Arbitrary-index DAE-trees
Documentation
For catalogs of functions provided by Integreat and links to function documentation, see the guide pages:
The tech notes provide some mathematical background, example code, and discussions about the package:
Examples
Compute properties of a Runge–Kutta method:
In[1]:=1
✖
https://wolfram.com/xid/0e2hzx1mgvi2drt4mimzyqq6-yo5rll
Out[2]=2
Out[3]=3
Out[4]=4
Out[5]=5
Out[6]=6
Out[7]=7
Out[8]=8
Derive the second order Adams–Bashforth method:
In[9]:=9
✖
https://wolfram.com/xid/0e2hzx1mgvi2drt4mimzyqq6-31loa5
Out[10]=10
Out[11]=11
Out[12]=12
Out[13]=13
Installation
Installing or upgrading Integreat is as simple as running
In[14]:=14
✖
https://wolfram.com/xid/0e2hzx1mgvi2drt4mimzyqq6-9ayqc
Once installed, Integreat subpackages can be loaded with
In[15]:=15
✖
https://wolfram.com/xid/0e2hzx1mgvi2drt4mimzyqq6-y6m864
Integreat can be uninstalled using
In[18]:=18
✖
https://wolfram.com/xid/0e2hzx1mgvi2drt4mimzyqq6-lp2zis