/
runge_kutta.c
executable file
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runge_kutta.c
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#include "dec.h"
#include "cosmic_rays.h"
#include "runge_kutta.h"
#include "read_parameters.h"
#include "synchrotron.h"
#include "jet.h"
/***********************************************************************/
/* Runge Kutta 2nd order, see Numerical Recipies §16*/
/* Auxiliary variable y2=dy1_dz*/
/* Convert second order equation into to ordinary diff eq.*/
void rk_2 (double h)
{
double k1_y, k2_y, k1_N, k2_N;
k1_y = h * d2N_dz2 (cr[i][j].z, cr[i][j].N, cr[i][j].y,
cr[i][j].E, cr[i][j].gamma, cr[i][j].dN_dE);
/* printf ("k1_y = %g", k1_y); */
/* exit(0); */
k1_N = h * cr[i][j].y;
k2_y = h * d2N_dz2 (cr[i][j].z + h / 2.0, cr[i][j].N + k1_N / 2.0,
cr[i][j].y + k1_y / 2.0,
cr[i][j].E, cr[i][j].gamma, cr[i][j].dN_dE);
k2_N = h * (cr[i][j].y + k1_y / 2.0);
cr[i+1][j].y = cr[i][j].y + k2_y;
cr[i+1][j].N = cr[i][j].N + k2_N;
// printf("rk_2: %d %g %g\n",i, x[i], rk[i+1].y1);
}
/***********************************************************************/
/* Runge Kutta 2nd order, see Numerical Recipies §16*/
/* Auxiliary variable y2=dy1_dz*/
/* Convert second order equation into to ordinary diff eq.*/
void rk_2_conv (double h)
{
double k1, k2;
k1 = h * dN_dz (cr[i][j].z, cr[i][j].N, cr[i][j].E, cr[i][j].gamma, cr[i][j].dN_dE);
k2 = h * dN_dz (cr[i][j].z + h / 2.0, cr[i][j].N + k1 / 2.0,
cr[i][j].E, cr[i][j].gamma, cr[i][j].dN_dE);
cr[i+1][j].N = cr[i][j].N + k2;
}
/**********************************************************************/
/***********************************************************************/
/* Runge Kutta 4th order, see Numerical Recipies §16*/
void rk_4(double h)
{
double k1_y, k2_y, k3_y, k4_y;
double k1_N, k2_N, k3_N, k4_N;
k1_y = h * d2N_dz2 (cr[i][j].z, cr[i][j].N, cr[i][j].y,
cr[i][j].E, cr[i][j].gamma, cr[i][j].dN_dE);
k1_N = h * (cr[i][j].y + k1_y);
k2_y = h * d2N_dz2 (cr[i][j].z + h / 2.0, cr[i][j].N + k1_N / 2.0,
cr[i][j].y + k1_y / 2.0,
cr[i][j].E, cr[i][j].gamma, cr[i][j].dN_dE);
k2_N = h * (cr[i][j].y + k2_y / 2.0);
k3_y = h * d2N_dz2 (cr[i][j].z + h / 2.0, cr[i][j].N + k2_N / 2.0,
cr[i][j].y + k2_y / 2.0,
cr[i][j].E, cr[i][j].gamma, cr[i][j].dN_dE);
k3_N = h * (cr[i][j].y + k2_y / 2.0);
k4_y = h * d2N_dz2 (cr[i][j].z + h, cr[i][j].N + k3_N,
cr[i][j].y + k3_y,
cr[i][j].E, cr[i][j].gamma, cr[i][j].dN_dE);
k4_N = h * (cr[i][j].y + k3_y);
cr[i+1][j].y = cr[i][j].y + k1_y / 6.0 + k2_y / 3.0 +
k3_y / 3.0 + k4_y / 6.0;
cr[i+1][j].N = cr[i][j].N + k1_N / 6.0 + k2_N / 3.0 +
k3_N / 3.0 + k4_N / 6.0;
}
/**********************************************************************/
/***********************************************************************/
void rk_4_conv(double h)
{
double k1_N, k2_N, k3_N, k4_N;
k1_N = h * dN_dz (cr[i][j].z, cr[i][j].N, cr[i][j].E,
cr[i][j].gamma, cr[i][j].dN_dE);
k2_N = h * dN_dz (cr[i][j].z + h / 2.0, cr[i][j].N + k1_N / 2.0,
cr[i][j].E, cr[i][j].gamma, cr[i][j].dN_dE);
k3_N = h * dN_dz (cr[i][j].z + h / 2.0, cr[i][j].N + k2_N / 2.0,
cr[i][j].E, cr[i][j].gamma, cr[i][j].dN_dE);
k4_N = h * dN_dz (cr[i][j].z + h, cr[i][j].N + k3_N,
cr[i][j].E, cr[i][j].gamma, cr[i][j].dN_dE);
cr[i+1][j].N = cr[i][j].N + k1_N / 6.0 + k2_N / 3.0 + k3_N / 3.0 + k4_N / 6.0;
}
/**********************************************************************/
/***********************************************************************/
/* Runge Kutta 4th order, see Numerical Recipies §16*/
void rk_4_cylindrical(double h)
{
double k1_y, k2_y, k3_y, k4_y;
double k1_N, k2_N, k3_N, k4_N;
if (cr[i][j].z == 0.0 && cr[i][j].y == 0.0)
k1_y = h * d2N_dz2 (cr[i][j].z, cr[i][j].N, cr[i][j].y,
cr[i][j].E, cr[i][j].gamma, cr[i][j].dN_dE);
else
k1_y = h * ( d2N_dz2 (cr[i][j].z, cr[i][j].N, cr[i][j].y,
cr[i][j].E, cr[i][j].gamma, cr[i][j].dN_dE) -
cr[i][j].y / cr[i][j].z );
k1_N = h * (cr[i][j].y + k1_y);
k2_y = h * ( d2N_dz2 (cr[i][j].z + h / 2.0, cr[i][j].N + k1_N / 2.0,
cr[i][j].y + k1_y / 2.0,
cr[i][j].E, cr[i][j].gamma, cr[i][j].dN_dE) -
(cr[i][j].y + k1_y / 2.0) / (cr[i][j].z + h / 2.0 ) );
k2_N = h * (cr[i][j].y + k2_y / 2.0);
k3_y = h * ( d2N_dz2 (cr[i][j].z + h / 2.0, cr[i][j].N + k2_N / 2.0,
cr[i][j].y + k2_y / 2.0,
cr[i][j].E, cr[i][j].gamma, cr[i][j].dN_dE) -
(cr[i][j].y + k2_y / 2.0) / (cr[i][j].z + h / 2.0) );
k3_N = h * (cr[i][j].y + k2_y / 2.0);
k4_y = h * ( d2N_dz2 (cr[i][j].z + h, cr[i][j].N + k3_N,
cr[i][j].y + k3_y,
cr[i][j].E, cr[i][j].gamma, cr[i][j].dN_dE) -
(cr[i][j].y + k3_y) / (cr[i][j].z + h) );
k4_N = h * (cr[i][j].y + k3_y);
cr[i+1][j].y = cr[i][j].y + k1_y / 6.0 + k2_y / 3.0 +
k3_y / 3.0 + k4_y / 6.0;
cr[i+1][j].N = cr[i][j].N + k1_N / 6.0 + k2_N / 3.0 +
k3_N / 3.0 + k4_N / 6.0;
}
/**********************************************************************/
/***********************************************************************/
/* Runge Kutta 4th order, see Numerical Recipies §16*/
void rk_4_radial(double h)
{
double k1_y, k2_y, k3_y, k4_y;
double k1_N, k2_N, k3_N, k4_N;
if (cr[i][j].z == 0.0 && cr[i][j].y == 0.0)
k1_y = h * d2N_dz2 (cr[i][j].z, cr[i][j].N, cr[i][j].y,
cr[i][j].E, cr[i][j].gamma, cr[i][j].dN_dE);
else
k1_y = h * ( d2N_dz2 (cr[i][j].z, cr[i][j].N, cr[i][j].y,
cr[i][j].E, cr[i][j].gamma, cr[i][j].dN_dE) -
2.0 * cr[i][j].y / cr[i][j].z );
k1_N = h * (cr[i][j].y + k1_y);
k2_y = h * ( d2N_dz2 (cr[i][j].z + h / 2.0, cr[i][j].N + k1_N / 2.0,
cr[i][j].y + k1_y / 2.0,
cr[i][j].E, cr[i][j].gamma, cr[i][j].dN_dE) -
2.0 * (cr[i][j].y + k1_y / 2.0) / (cr[i][j].z + h / 2.0 ) );
k2_N = h * (cr[i][j].y + k2_y / 2.0);
k3_y = h * ( d2N_dz2 (cr[i][j].z + h / 2.0, cr[i][j].N + k2_N / 2.0,
cr[i][j].y + k2_y / 2.0,
cr[i][j].E, cr[i][j].gamma, cr[i][j].dN_dE) -
2.0 * (cr[i][j].y + k2_y / 2.0) / (cr[i][j].z + h / 2.0) );
k3_N = h * (cr[i][j].y + k2_y / 2.0);
k4_y = h * ( d2N_dz2 (cr[i][j].z + h, cr[i][j].N + k3_N,
cr[i][j].y + k3_y,
cr[i][j].E, cr[i][j].gamma, cr[i][j].dN_dE) -
2.0 * (cr[i][j].y + k3_y) / (cr[i][j].z + h) );
k4_N = h * (cr[i][j].y + k3_y);
cr[i+1][j].y = cr[i][j].y + k1_y / 6.0 + k2_y / 3.0 +
k3_y / 3.0 + k4_y / 6.0;
cr[i+1][j].N = cr[i][j].N + k1_N / 6.0 + k2_N / 3.0 +
k3_N / 3.0 + k4_N / 6.0;
}
/***********************************************************************/
void rk_4_conv_1(double h)
{
cr[i][j].k1_N = h * dN_dz (cr[i][j].z, cr[i][j].N, cr[i][j].E,
cr[i][j].gamma, cr[i][j].dN_dE);
}
/***********************************************************************/
void rk_4_conv_2(double h)
{
double dN_dE_rk;
cr[i][j].gamma_rk = - log ( (cr[i][j+1].N + cr[i][j+1].k1_N / 2.0) / (cr[i][j-1].N + cr[i][j-1].k1_N / 2.0) ) /
log (cr[i][j+1].E / cr[i][j-1].E);
cr[i][j].dN_dE_rk = ( (cr[i][j+1].N + cr[i][j+1].k1_N / 2.0) - (cr[i][j-1].N + cr[i][j-1].k1_N / 2.0) ) /
(cr[i][j+1].E - cr[i][j-1].E);
if (j==nu_channel+1)
{
cr[i][j].gamma_rk = 2.0 * cr[i][j-1].gamma_rk - cr[i][j-2].gamma_rk;
cr[i][j].dN_dE_rk = ( (cr[i][j].N + cr[i][j].k1_N / 2.0) - (cr[i][j-1].N + cr[i][j-1].k1_N / 2.0) ) /
(cr[i][j].E - cr[i][j-1].E);
}
if (j==0)
{
cr[i][j].gamma_rk = 2.0 * cr[i][1].gamma_rk - cr[i][2].gamma_rk;
cr[i][j].dN_dE_rk = ( (cr[i][j+1].N + cr[i][j+1].k1_N / 2.0) - (cr[i][j].N + cr[i][j].k1_N / 2.0) ) /
(cr[i][j+1].E - cr[i][j].E);
}
// if (j==0)
// printf ("Conv2: i = %d gamma=%g\n", i, cr[i][1].gamma_rk);
// if (j==nu_channel)
// printf ("conv2: gamma_rk = %g, gamma = %g \n", cr[i][j].gamma_rk, cr[i][j].gamma);
cr[i][j].k2_N = h * dN_dz (cr[i][j].z + h / 2.0, cr[i][j].N + cr[i][j].k1_N / 2.0,
cr[i][j].E, cr[i][j].gamma_rk, cr[i][j].dN_dE_rk);
// if (j==50)
// printf ("i = %d conv2: N = %g\n", i, cr[i][j].k2_N);
}
/***********************************************************************/
void rk_4_conv_3(double h)
{
double dN_dE_rk;
cr[i][j].gamma_rk = - log ( (cr[i][j+1].N + cr[i][j+1].k2_N / 2.0) / (cr[i][j-1].N + cr[i][j-1].k2_N / 2.0) ) /
log (cr[i][j+1].E / cr[i][j-1].E);
cr[i][j].dN_dE_rk = ( (cr[i][j+1].N + cr[i][j+1].k2_N / 2.0) - (cr[i][j-1].N + cr[i][j-1].k2_N / 2.0) ) /
(cr[i][j+1].E - cr[i][j-1].E);
if (j==nu_channel+1)
{
cr[i][j].gamma_rk = 2.0 * cr[i][j-1].gamma_rk - cr[i][j-2].gamma_rk;
cr[i][j].dN_dE_rk = ( (cr[i][j].N + cr[i][j].k2_N / 2.0) - (cr[i][j-1].N + cr[i][j-1].k2_N / 2.0) ) /
(cr[i][j].E - cr[i][j-1].E);
}
if (j==0)
{
cr[i][j].gamma_rk = 2.0 * cr[i][1].gamma_rk - cr[i][2].gamma_rk;
cr[i][j].dN_dE_rk = ( (cr[i][j+1].N + cr[i][j+1].k2_N / 2.0) - (cr[i][j].N + cr[i][j].k2_N / 2.0) ) /
(cr[i][j+1].E - cr[i][j].E);
}
// if (j==nu_channel)
// printf ("conv3: gamma_rk = %g, gamma = %g \n", cr[i][j].gamma_rk, cr[i][j].gamma);
cr[i][j].k3_N = h * dN_dz (cr[i][j].z + h / 2.0, cr[i][j].N + cr[i][j].k2_N / 2.0,
cr[i][j].E, cr[i][j].gamma_rk, cr[i][j].dN_dE_rk);
// if (j==50)
// printf ("i = %d conv3: N = %g\n", i, cr[i][j].k3_N);
}
/***********************************************************************/
void rk_4_conv_4(double h)
{
double dN_dE_rk;
cr[i][j].gamma_rk = - log ( (cr[i][j+1].N + cr[i][j+1].k3_N) / (cr[i][j-1].N + cr[i][j-1].k3_N) ) /
log (cr[i][j+1].E / cr[i][j-1].E);
cr[i][j].dN_dE_rk = ( (cr[i][j+1].N + cr[i][j+1].k3_N) - (cr[i][j-1].N + cr[i][j-1].k3_N) ) /
(cr[i][j+1].E - cr[i][j-1].E);
if (j==nu_channel+1)
{
cr[i][j].gamma_rk = 2.0 * cr[i][j-1].gamma_rk - cr[i][j-2].gamma_rk;
cr[i][j].dN_dE_rk = ( (cr[i][j].N + cr[i][j].k3_N) - (cr[i][j-1].N + cr[i][j-1].k3_N) ) /
(cr[i][j].E - cr[i][j-1].E);
}
if (j==0)
{
cr[i][j].gamma_rk = 2.0 * cr[i][1].gamma_rk - cr[i][2].gamma_rk;
cr[i][j].dN_dE_rk = ( (cr[i][j+1].N + cr[i][j+1].k3_N) - (cr[i][j].N + cr[i][j].k3_N) ) /
(cr[i][j+1].E - cr[i][j].E);
}
// if (j==nu_channel)
// printf ("conv4: gamma_rk = %g, gamma = %g \n", cr[i][j].gamma_rk, cr[i][j].gamma);
cr[i][j].k4_N = h * dN_dz (cr[i][j].z + h / 2.0, cr[i][j].N + cr[i][j].k3_N,
cr[i][j].E, cr[i][j].gamma_rk, cr[i][j].dN_dE_rk);
// if (j==50)
// printf ("i = %d conv4: N = %g\n", i, cr[i][j].k4_N);
cr[i+1][j].N = cr[i][j].N + cr[i][j].k1_N / 6.0 + cr[i][j].k2_N / 3.0 + cr[i][j].k3_N / 3.0 + cr[i][j].k4_N / 6.0;
// if (j==50)
// printf ("i = %d conv4: N+1 = %g\n", i, cr[i+1][j].N);
}