Re: Solving a non-linear system to find coefficients in

*To*: mathgroup at smc.vnet.net*Subject*: [mg113016] Re: Solving a non-linear system to find coefficients in*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Mon, 11 Oct 2010 05:16:01 -0400 (EDT)

Needs["NumericalDifferentialEquationAnalysis`"] sys = RungeKuttaOrderConditions[4, 4, ButcherRowSum -> True, RungeKuttaMethod -> Explicit] /. {c[2] -> 1/2, a[3, 1] -> 0} // Flatten; SplitBy[soln = Reduce[sys] // ToRules // Sort, Head[#[[1]]] &] {{a[2, 1] -> 1/2, a[3, 2] -> 1/2, a[4, 1] -> 0, a[4, 2] -> 0, a[4, 3] -> 1}, {b[1] -> 1/6, b[2] -> 1/3, b[3] -> 1/3, b[4] -> 1/6}, {c[3] -> 1/2, c[4] -> 1}} And @@ (sys /. soln) True Bob Hanlon ---- Allamarein <matteo.diplomacy at gmail.com> wrote: ============= 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