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Re: [Help-gsl] RK4 Help required

From: Pau Cervera Badia
Subject: Re: [Help-gsl] RK4 Help required
Date: Tue, 08 May 2007 11:26:20 +0200
User-agent: Thunderbird (X11/20070403)

Since gsl solvers solve systems of first order differential equations of the type:

x' = f(x,t) (where the prima is the time derivative)

where x is a vector of positions, and f(x,t) is the vector of forces you have to implement via the func that is passed via gsl_odeiv_system to the gsl solver, you should consider making a vector x of 3 times longer than the number of charges you have.

For instance, you can order your components in a 12-vector as,

x_0, y_0, z_0, x_1, y_1, z_1, x_2, y_2, z_2, x_3, y_3, z_3.

To help you to extract the right components, you can define the macros,

#define xindex(i) 3 * i
#define yindex(i) 3 * i + 1
#define zindex(z) 3 * i + 2

and access the position of particle i as

double x_i = sys[xindex(i)];
double y_i = sys[yindex(i)];
double z_i = sys[zindex(i)];

when needed.

Good luck,

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
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.
Thanks for your time,

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Pau Cervera i Badia (e-mail address@hidden)
  Departament de Física Fonamental               Martí i Franqués, 1
  Universitat de Barcelona                 Planta 3, despatx 346 bis
                                                     08028 Barcelona
  tel: +34 934 039 708                                         Spain

  "Simple things should be simple, complex things should be possible."
                                                           -- Alan Kay

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