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

• To: mathgroup at smc.vnet.net
• Subject: [mg113046] Re: Solving a non-linear system to find coefficients in Runge-Kutta method
• From: Allamarein <matteo.diplomacy at gmail.com>
• Date: Tue, 12 Oct 2010 04:25:10 -0400 (EDT)
• References: <i8s5b4$90h$1@smc.vnet.net> <i8uko2$ofb$1@smc.vnet.net>

I thank you for helping me.
I am learning how I must use Mathematica.
Anyway I am not able yet to extend this procedure to find the
coefficients for 6th, 7th and 8th order Runge-Kutta.
The problem is more related with the math, than with Mathematica.
As a matter of fact I know I have to impose 2 conditions for the 4th
order, but I don't know how many conditions I should give for higher
order.
Perhaps I should see how many equations and unknowns are given by
RungeKutta OrderConditions, but I am not able to do that.
Furthermore I should choose the right values...

Is someone able to find the coefficients for the above-mentioned
orders?