Solving a non-linear system to find coefficients in Runge-Kutta method

*To*: mathgroup at smc.vnet.net*Subject*: [mg112994] Solving a non-linear system to find coefficients in Runge-Kutta method*From*: Allamarein <matteo.diplomacy at gmail.com>*Date*: Sun, 10 Oct 2010 06:41:31 -0400 (EDT)

I have just launched: RungeKuttaOrderConditions[4, 4, ButcherRowSum -> True, RungeKuttaMethod -> Explicit] Well done: I get a set of 11 non-linear equations with 13 unknows, like theory predicts. I can choice c(2) = 1/2 and a(3,1) = 0, so I have 11 eqs. and 11unkns. Anyway, how can I solve this system in Mathematica? I need to find the elements of matrix a and of vector b and c. This is only an example. If I could solve the previous problem, I would extend that procedure to RK6 or RK8