I understand that ode45 uses Dormand-Prince method to generate the solution at the adaptive time steps. So in the case when tspan input is with more than two elements, the documentation points out that it doesn't affect internal time step. So even though it returns the answer at the specified tspan values, it's not guaranteed that the solver stepped exactly to those values but rather somewhere close, since it's adaptive in nature. My question is what does it use to produce the answer at the desired node since the solver didn't step there? What are the details of this interpolation scheme?
This is the documentation found in the help for ode45 (below):
Specifying tspan with more than two elements does not affect the internal time steps that the solver uses to traverse the interval from tspan(1) to tspan(end). (All solvers in the ODE suite obtain output values by means of continuous extensions of the basic formulas) [WHAT DOES THIS SENTENCE MEAN?!]. (Although a solver does not necessarily step precisely to a time point specified in tspan, the solutions produced at the specified time points are of the same order of accuracy as the solutions computed at the internal time points) [WHAT METHOD IS USED FOR THIS? TO GET THE SAME ORDER OF ACCURACY].
Thanks in advance!
Thanks for the help!
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