I want to solve only one equation by RK4Rich function, but doesn't work ok.

Sorry for answering so late, I'm actually too busy at the moment...

I think

RK4Rich does not work properly because you forgot the output argument

y, which is mandatory; you just used the optional output, but mandatory output should be present as well, even if you don't need it. Try this:

T,tp,Tp=RK4Rich(RHS,t0,{T0},tf,true,5*10^-4)

I bet

RK4Rich will work then. If not, double-check your

RHS function, and make sure it implements the right-hand side of the differential equation you want to solve.

then what is the ?Rich function?? please explain without the abbreviations so maybe some one can help you.

"Rich" is

*not* a function written by girdeuax, it's part of the name of the LNA function. "Rich" comes from "Richardson extrapolation". Remember,

RK4Rich is not just an implementation of the Runge-Kutta method of fourth order; it also uses adaptive stepsize control (via Richardson extrapolation). Runge-Kutta method without stepsize control is not available in LNA, and it will never be, since constant integration step is a common source of inaccurate results.

Anyway, your question should be posted at the LNA topic, not here....