Using different ODE solvers in Matlab and getting same solutions - how to interpret this?

Question

I typically use ode45 in Matlab but recently experimented with other ode solvers in Matlab and am still getting the same solutions. What does this say about the solutions, if anything at all?

Are the solutions "consistent"? "Stable"? "Trustworthy"?

Or does it really say something about ode45 being a "reliable" solver for the equations of interest?

Answer 1

It probably says that your equations/systems are "nice". They are probably not stiff, or some solvers would have trouble. (In fact ode45 is not for stiff systems. Stiff roughly means having solution components with widely differing time scales so that neither scale is suitable for following the other component -- for instance, having a millisecond transient on a Megasecond period signal.) More on this in the documentation.