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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
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