int main(void)
{
int i;
float b1,b2,b3,b4,xf=X1+HTOT,*y,*yout,*dydx;
y=vector(1,NVAR);
yout=vector(1,NVAR);
dydx=vector(1,NVAR);
y[1]=bessj0(X1);
y[2]=bessj1(X1);
y[3]=bessj(2,X1);
y[4]=bessj(3,X1);
derivs(X1,y,dydx);
b1=bessj0(xf);
b2=bessj1(xf);
b3=bessj(2,xf);
b4=bessj(3,xf);
printf("First four Bessel functions:\n");
for (i=5;i<=50;i+=5) {
mmid(y,dydx,NVAR,X1,HTOT,i,yout,derivs);
printf("\n%s %5.2f %s %5.2f %s %2d %s \n",
"x=",X1," to ",X1+HTOT," in ",i," steps");
printf("%14s %9s\n","integration","bessj");
printf("%12.6f %12.6f\n",yout[1],b1);
printf("%12.6f %12.6f\n",yout[2],b2);
printf("%12.6f %12.6f\n",yout[3],b3);
printf("%12.6f %12.6f\n",yout[4],b4);
printf("\nPress RETURN to continue...\n");
(void) getchar();
}
free_vector(dydx,1,NVAR);
free_vector(yout,1,NVAR);
free_vector(y,1,NVAR);
return 0;
}
int main(void)
{
int i,j;
float h,x=1.0,*y,*dydx,*yout;
y=vector(1,N);
dydx=vector(1,N);
yout=vector(1,N);
y[1]=bessj0(x);
y[2]=bessj1(x);
y[3]=bessj(2,x);
y[4]=bessj(3,x);
derivs(x,y,dydx);
printf("\n%16s %5s %12s %12s %12s\n",
"Bessel function:","j0","j1","j3","j4");
for (i=1;i<=5;i++) {
h=0.2*i;
rk4(y,dydx,N,x,h,yout,derivs);
printf("\nfor a step size of: %6.2f\n",h);
printf("%12s","rk4:");
for (j=1;j<=4;j++) printf(" %12.6f",yout[j]);
printf("\n%12s %12.6f %12.6f %12.6f %12.6f\n","actual:",
bessj0(x+h),bessj1(x+h),bessj(2,x+h),bessj(3,x+h));
}
free_vector(yout,1,N);
free_vector(dydx,1,N);
free_vector(y,1,N);
return 0;
}
void bessy01(real_t x, real_t *y0, real_t *y1)
{
if (x < 8.0) {
int i;
real_t bessj0(real_t);
real_t bessj1(real_t);
real_t z,z2,c,lnx,b0,b1,b2;
static real_t ar1[15]={0.164349e-14, -0.8747341e-13,
0.402633082e-11, -0.15837552542e-9, 0.524879478733e-8,
-0.14407233274019e-6, 0.32065325376548e-5,
-0.563207914105699e-4, 0.753113593257774e-3,
-0.72879624795521e-2, 0.471966895957634e-1,
-0.177302012781143, 0.261567346255047,
0.179034314077182, -0.274474305529745};
static real_t ar2[15]={0.42773e-15, -0.2440949e-13,
0.121143321e-11, -0.5172121473e-10, 0.187547032473e-8,
-0.5688440039919e-7, 0.141662436449235e-5,
-0.283046401495148e-4, 0.440478629867099e-3,
-0.51316411610611e-2, 0.423191803533369e-1,
-0.226624991556755, 0.675615780772188,
-0.767296362886646, -0.128697384381350};
c=0.636619772367581;
lnx=c*log(x);
c /= x;
x /= 8.0;
z=2.0*x*x-1.0;
z2=z+z;
b1=b2=0.0;
for (i=0; i<=14; i++) {
b0=z2*b1-b2+ar1[i];
b2=b1;
b1=b0;
}
*y0 = lnx*bessj0(8.0*x)+z*b1-b2-0.33146113203285e-1;
b1=b2=0.0;
for (i=0; i<=14; i++) {
b0=z2*b1-b2+ar2[i];
b2=b1;
b1=b0;
}
*y1 = lnx*bessj1(8.0*x)-c+x*(z*b1-b2+0.2030410588593425e-1);
} else {
void besspq0(real_t, real_t *, real_t *);
void besspq1(real_t, real_t *, real_t *);
real_t c,cosx,sinx,p0,q0,p1,q1;
c=0.797884560802865/sqrt(x);
besspq0(x,&p0,&q0);
besspq1(x,&p1,&q1);
x -= 0.706858347057703e1;
cosx=cos(x);
sinx=sin(x);
*y0 = c*(p0*sinx+q0*cosx);
*y1 = c*(q1*sinx-p1*cosx);
}
}
int main(void)
{
int i,j;
float eps,hdid,hnext,htry,x=1.0,*y,*dydx,*dysav,*ysav,*yscal;
y=vector(1,N);
dydx=vector(1,N);
dysav=vector(1,N);
ysav=vector(1,N);
yscal=vector(1,N);
ysav[1]=bessj0(x);
ysav[2]=bessj1(x);
ysav[3]=bessj(2,x);
ysav[4]=bessj(3,x);
derivs(x,ysav,dysav);
for (i=1;i<=N;i++) yscal[i]=1.0;
htry=0.6;
printf("%10s %11s %12s %13s\n","eps","htry","hdid","hnext");
for (i=1;i<=15;i++) {
eps=exp((double) -i);
x=1.0;
for (j=1;j<=N;j++) {
y[j]=ysav[j];
dydx[j]=dysav[j];
}
rkqs(y,dydx,N,&x,htry,eps,yscal,&hdid,&hnext,derivs);
printf("%13f %8.2f %14.6f %12.6f \n",eps,htry,hdid,hnext);
}
free_vector(yscal,1,N);
free_vector(ysav,1,N);
free_vector(dysav,1,N);
free_vector(dydx,1,N);
free_vector(y,1,N);
return 0;
}
float bessy1(float x)
{
float bessj1(float x);
float z;
double xx,y,ans,ans1,ans2;
if (x < 8.0) {
y=x*x;
ans1=x*(-0.4900604943e13+y*(0.1275274390e13
+y*(-0.5153438139e11+y*(0.7349264551e9
+y*(-0.4237922726e7+y*0.8511937935e4)))));
ans2=0.2499580570e14+y*(0.4244419664e12
+y*(0.3733650367e10+y*(0.2245904002e8
+y*(0.1020426050e6+y*(0.3549632885e3+y)))));
ans=(ans1/ans2)+0.636619772*(bessj1(x)*log(x)-1.0/x);
} else {
z=8.0/x;
y=z*z;
xx=x-2.356194491;
ans1=1.0+y*(0.183105e-2+y*(-0.3516396496e-4
+y*(0.2457520174e-5+y*(-0.240337019e-6))));
ans2=0.04687499995+y*(-0.2002690873e-3
+y*(0.8449199096e-5+y*(-0.88228987e-6
+y*0.105787412e-6)));
ans=sqrt(0.636619772/x)*(sin(xx)*ans1+z*cos(xx)*ans2);
}
return ans;
}
int main(void)
{
int i,nbad,nok;
float eps=1.0e-4,h1=0.1,hmin=0.0,x1=1.0,x2=10.0,*ystart;
ystart=vector(1,N);
xp=vector(1,200);
yp=matrix(1,10,1,200);
ystart[1]=bessj0(x1);
ystart[2]=bessj1(x1);
ystart[3]=bessj(2,x1);
ystart[4]=bessj(3,x1);
nrhs=0;
kmax=100;
dxsav=(x2-x1)/20.0;
odeint(ystart,N,x1,x2,eps,h1,hmin,&nok,&nbad,derivs,rkqs);
printf("\n%s %13s %3d\n","successful steps:"," ",nok);
printf("%s %20s %3d\n","bad steps:"," ",nbad);
printf("%s %9s %3d\n","function evaluations:"," ",nrhs);
printf("\n%s %3d\n","stored intermediate values: ",kount);
printf("\n%8s %18s %15s\n","x","integral","bessj(3,x)");
for (i=1;i<=kount;i++)
printf("%10.4f %16.6f %14.6f\n",
xp[i],yp[4][i],bessj(3,xp[i]));
free_matrix(yp,1,10,1,200);
free_vector(xp,1,200);
free_vector(ystart,1,N);
return 0;
}
int main(void)
{
char txt[MAXSTR];
int i,nval;
float val,x;
FILE *fp;
if ((fp = fopen("fncval.dat","r")) == NULL)
nrerror("Data file fncval.dat not found\n");
fgets(txt,MAXSTR,fp);
while (strncmp(txt,"Bessel Function J1",18)) {
fgets(txt,MAXSTR,fp);
if (feof(fp)) nrerror("Data not found in fncval.dat\n");
}
fscanf(fp,"%d %*s",&nval);
printf("\n%s\n",txt);
printf("%5s %12s %13s \n","x","actual","bessj1(x)");
for (i=1;i<=nval;i++) {
fscanf(fp,"%f %f",&x,&val);
printf("%6.2f %12.7f %12.7f\n",x,val,bessj1(x));
}
fclose(fp);
return 0;
}
float dfunc(float x)
{
return -bessj1(x);
}
