Error tolerance in ODE45

What's the role of the error tolerance in ode45? What does it do?

Answer 1

[Steven Lord]

Are you referring to the options in the Error Control option group in the table on this documentation page? If you click on the name of the option you will be taken to the section of the odeset documentation page discussing that option. After reading the sections on RelTol, AbsTol, and NormControl do you have a specific question about one or all of those options?

You might also find pages 11-13 of the paper "The MATLAB ODE Suite" included in the PDF documentation and the chapter on ODEs in Cleve Moler's Numerical Computing with MATLAB informative.

[Buttercup12]

Your answer helped to clear some things up, but I got another follow-up question. From one of the sources you gave me I found this:

"To be successful, the step must have acceptable error, as determined by both the relative and absolute error tolerances..."

What happes if the step doesn't have an acceptable error? Is the step adjusted?

[Steven Lord]

Yes. ode45 uses an adaptive Runge-Kutta method. If the estimated error is not below tolerance the ODE solver will adapt by rejecting the step it just tried and trying a smaller step.