Timestepping controller names

[dtretiak]

Question❓

tldr; I believe the standard timestepping controller should be called the proportional controller rather than the integral controller

In the Timestepping Method Descriptions page the standard controller is called the Integral Controller. However, what is described sounds much more like a proportional controller. The page later goes on to describe a PI controller as a proportional controller with memory further sounding like the first one should be called a P controller rather than an I controller.

[ChrisRackauckas]

I thought it was a PController but I think it was @ranocha that said it was actually an IController, but I cannot find his reasoning on that.

[ranocha]

See Hairer and Wanner (2010) Solving Ordinary Differential Equations II, Section IV.2, Paragraph "A PI Step Size Control", pages 28 and 29. The standard controller uses only the error estimate from the previous step, which corresponds to the "integral term" with parameter $n_1$ in their description.