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Does the Stiffness switching method with NDsolve switch just between multiple variants of 4th order Runge Kutta method or it uses also other methods?

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closed as off-topic by 2012rcampion, bbgodfrey, Mike Honeychurch, Dr. belisarius, J. M. is away May 15 '15 at 3:07

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    $\begingroup$ The only way to overcome stiffness phenomenon is to switch to a suitable implicit scheme. Switching between explicit RK methods is pointless $\endgroup$ – uranix May 14 '15 at 23:31
  • $\begingroup$ Stiffness switching is extensively documented in the Stiffness Detection tutorial. $\endgroup$ – 2012rcampion May 15 '15 at 0:28
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    $\begingroup$ If you'd read the docs, you'd have been able to note that Mathematica uses a method appropriate for nonstiff systems by default, and switches to a stiff method every time the built-in detector is tripped. Furthermore, by default, "StiffnessSwitching" uses a pair of Bulirsch-Stoer methods for the stiff and nonstiff methods. But really… read the docs! (And then maybe read Hairer/Nørsett/Wanner afterwards.) $\endgroup$ – J. M. is away May 15 '15 at 0:32
  • $\begingroup$ @uranix, implicit schemes are stable instead of explicit methods. But is there another method? Can we get a.no-stiff equations to the same problem with change variables or other methods? $\endgroup$ – tanghe2014 Dec 13 '16 at 8:44