double rk_main(double alpha,double epsilon,double h_init){
double x=0,y=1,y4,y5,h=h_init;
double a[6][6],b5[6],b4[6],c[6];
set_a(a);
set_b4(b4);
set_b5(b5);
set_c(c);
printf("#\t%s\t%s\t%s\t%s\n","x","y","h","dy/dx");
while(x<10.0){
rk_step(x,y,h,a,b4,c,&y4);
rk_step(x,y,h,a,b5,c,&y5);
if(y4-y5<epsilon){
printf("\t%f\t%f\t%e\t%f\n",x,y,h,f(x));
x+=h;
y=y5;
h=alpha*h*pow(epsilon/fabs(y4-y5),0.2);
}else{
h=h/2;
}
}
return y;
}
int
gsl_sf_bessel_sequence_Jnu_e(double nu, gsl_mode_t mode, size_t size, double * v)
{
/* CHECK_POINTER(v) */
if(nu < 0.0) {
GSL_ERROR ("domain error", GSL_EDOM);
}
else if(size == 0) {
GSL_ERROR ("error", GSL_EINVAL);
}
else {
const gsl_prec_t goal = GSL_MODE_PREC(mode);
const double dx_array[] = { 0.001, 0.03, 0.1 }; /* double, single, approx */
const double dx_nominal = dx_array[goal];
const int cnu = (int) ceil(nu);
const double nu13 = pow(nu,1.0/3.0);
const double smalls[] = { 0.01, 0.02, 0.4, 0.7, 1.3, 2.0, 2.5, 3.2, 3.5, 4.5, 6.0 };
const double x_small = ( nu >= 10.0 ? nu - nu13 : smalls[cnu] );
gsl_sf_result J0, J1;
double Jp, J;
double x;
size_t i = 0;
/* Calculate the first point. */
x = v[0];
gsl_sf_bessel_Jnu_e(nu, x, &J0);
v[0] = J0.val;
++i;
/* Step over the idiot case where the
* first point was actually zero.
*/
if(x == 0.0) {
if(v[1] <= x) {
/* Strict ordering failure. */
GSL_ERROR ("error", GSL_EFAILED);
}
x = v[1];
gsl_sf_bessel_Jnu_e(nu, x, &J0);
v[1] = J0.val;
++i;
}
/* Calculate directly as long as the argument
* is small. This is necessary because the
* integration is not very good there.
*/
while(v[i] < x_small && i < size) {
if(v[i] <= x) {
/* Strict ordering failure. */
GSL_ERROR ("error", GSL_EFAILED);
}
x = v[i];
gsl_sf_bessel_Jnu_e(nu, x, &J0);
v[i] = J0.val;
++i;
}
/* At this point we are ready to integrate.
* The value of x is the last calculated
* point, which has the value J0; v[i] is
* the next point we need to calculate. We
* calculate nu+1 at x as well to get
* the derivative, then we go forward.
*/
gsl_sf_bessel_Jnu_e(nu+1.0, x, &J1);
J = J0.val;
Jp = -J1.val + nu/x * J0.val;
while(i < size) {
const double dv = v[i] - x;
const int Nd = (int) ceil(dv/dx_nominal);
const double dx = dv / Nd;
double xj;
int j;
if(v[i] <= x) {
/* Strict ordering failure. */
GSL_ERROR ("error", GSL_EFAILED);
}
/* Integrate over interval up to next sample point.
*/
for(j=0, xj=x; j<Nd; j++, xj += dx) {
rk_step(nu, xj, dx, &Jp, &J);
}
/* Go to next interval. */
x = v[i];
v[i] = J;
++i;
}
return GSL_SUCCESS;
}
}