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;
}
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;
}
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,n;
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 Jn",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("%4s %7s %15s %20s \n","n","x","actual","bessj(n,x)");
for (i=1;i<=nval;i++) {
fscanf(fp,"%d %f %f",&n,&x,&val);
printf("%4d %8.2f %18.6e %18.6e\n",n,x,val,bessj(n,x));
}
fclose(fp);
return 0;
}