I used automatic method for NDSolve. Then I asked myself - which method Mathemathica prefered? I got an answer for this question on this forum, that I need to use:
Select[Flatten[
Trace[NDSolve[{g[a[t]]*a''[t] + 0.5*dg[a[t]]*(a'[t])^2 + dV[a[t]] ==
0, a[0] == a0, a'[0] == -u}, a, {t, 0, t0}],
TraceInternal -> True]], ! FreeQ[#, Method | NDSolve`MethodData] &]
I got a long answer from Mathematica, from which I show you only two main unique strings:
NDSolve`InitializeMethod[NDSolve'LSODA,{Automatic, Automatic} ...
NDSolve`LSODA[NDSolve`MethodData[4, 22, {{}, False, 12, {NDSolve`Newton,{Automatic}}, None, False}]]
I understood, that Mathematica has chosen for method: LSODA and it's submethod: Newton. Whether I'm correct or this methods have another name? And what does LSODA stand for?
NDSolve
was choosing LSODA, you can find several places where it is mentioned by searching for LSODA in the documentation. One prominent place to look for some more information and references is (stiffness detection)[reference.wolfram.com/mathematica/tutorial/…. The advanced documentation forNDSolve
(use this string in the documentation center search field: tutorial/NDSolveOverview) is quite detailed and well worth reading... $\endgroup$ – Albert Retey Apr 20 '14 at 8:32