Ode45 step size evaluation procedure

Hello,

I've been trying to work out how the ode45 command in matlab evaluates whether the step size is appropriate. I was under the impression that solutions were calculated at the 4th and 5th orders using the rkf45 method and then compared to see if the error is within acceptable, pre-specified, bounds. If the error is greater, the step size is reduced and vice versa.

Is this true or is another method followed?

[James Tursa]

I don't know if the details of this are published anywhere, but my assumption would be the similar to yours ... that the 5th order estimated error terms are generated and compared to the 4th order, etc.

[Ameer Hamza]

The documentation page reference these papers for the algorithm. Going through them might be helpful:

https://pdf.sciencedirectassets.com/271610/1-s2.0-S0771050X00X00216/1-s2.0-0771050X80900133

https://www.mathworks.com/help/pdf_doc/otherdocs/ode_suite.pdf