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## Re: [Help-gsl] RK4 Help required

 From: Simpson, Kenneth Subject: Re: [Help-gsl] RK4 Help required Date: Thu, 10 May 2007 09:45:17 -0700

```If the charges are electrical charges, typically one looks
at the resultant force on one of charges due to the other
charges.

Hence, for a particular i, say i=1, one sums the forces on i
due to other j charges, namely, j=2,3,4.

And if you're looking for x(t) for the charges, you need to
write the the 2nd order force equation as two coupled 1st order
equations:

dv/dt=Columb's Law
dx/dt=v

-- Ken

cigdem ozkan wrote:
> Hi again,
> I am posting a smaller version of my question rearding rk4 since I didnt get
> a reply and I am really anxious for some feedback.
>
> I have the following fuction:
> dxi/dt = k*qi*(xi-xj)/sqrt((xi-xj)2+(yi-yj)2+(zi-zj)2)
> where qi is the charge of the i-th particle, xi, yi, zi are the coordinates
> of the i-th particle and xj, yj,zj are the coordinates of the j-th particle.
> Input for the initial values: q[4] =  { 1.0, 1.0, -1.0, 1.0 } charge x0[4] =
> { 1.0, 2.3, 3.2, 4.0 } init posn x
> y0[4] = { 1.0, 2.4, 3.0, 4.0 } init posn y
> z0[4] = { 1.0, 2.5, 3.3, 4.2 } init posn z
> QUESTION:
> Since there are two values for each coordinate (i and j), how can I write the
> function in an acceptable form for RK4? I would appreciate any feedback
> concerning RK4.
> C.
>
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